diff --git a/docs/reference/accessors.rst b/docs/reference/accessors.rst
index 9682181..5927321 100644
--- a/docs/reference/accessors.rst
+++ b/docs/reference/accessors.rst
@@ -12,4 +12,7 @@ Accessors
    ArrayAccessor.union
    ArrayAccessor.intersection
    ArrayAccessor.difference
-   ArrayAccessor.symmetric_difference
\ No newline at end of file
+   ArrayAccessor.symmetric_difference
+   ArrayAccessor.isdisjoint
+   ArrayAccessor.issuperset
+   ArrayAccessor.issubset
\ No newline at end of file
diff --git a/docs/reference/interval.rst b/docs/reference/interval.rst
index bd67928..a8ec10c 100644
--- a/docs/reference/interval.rst
+++ b/docs/reference/interval.rst
@@ -12,4 +12,6 @@ Interval
    union
    intersection
    difference
-   symmetric_difference
\ No newline at end of file
+   symmetric_difference
+   issuperset
+   issubset
\ No newline at end of file
diff --git a/docs/reference/package.rst b/docs/reference/package.rst
index bfc4708..b0f4af1 100644
--- a/docs/reference/package.rst
+++ b/docs/reference/package.rst
@@ -14,4 +14,7 @@ Top level functions
    union
    intersection
    difference
-   symmetric_difference
\ No newline at end of file
+   symmetric_difference
+   isdisjoint
+   issuperset
+   issubset
\ No newline at end of file
diff --git a/docs/release_notes/index.rst b/docs/release_notes/index.rst
index 7873be7..ff5bc83 100644
--- a/docs/release_notes/index.rst
+++ b/docs/release_notes/index.rst
@@ -4,6 +4,24 @@
 Release notes
 ========================
 
+
+ADD UNRELEASED CHANGES ABOVE THIS LINE
+
+
+**v0.2.0 2021-10-15**
+
+Added the following methods
+
+- :meth:`piso.isdisjoint`
+- :meth:`piso.issuperset`
+- :meth:`piso.issubset`
+- :meth:`ArrayAccessor.isdisjoint() <piso.accessor.ArrayAccessor.isdisjoint>`
+- :meth:`ArrayAccessor.issuperset() <piso.accessor.ArrayAccessor.issuperset>`
+- :meth:`ArrayAccessor.issubset() <piso.accessor.ArrayAccessor.issubset>`
+- :meth:`piso.interval.issuperset`
+- :meth:`piso.interval.issubset`
+
+
 **v0.1.0 2021-10-10**
 
 The following methods are included in the initial release of `piso`
@@ -13,7 +31,12 @@ The following methods are included in the initial release of `piso`
 - :meth:`piso.intersection`
 - :meth:`piso.difference`
 - :meth:`piso.symmetric_difference`
+- :meth:`ArrayAccessor.union() <piso.accessor.ArrayAccessor.union>`
+- :meth:`ArrayAccessor.intersection() <piso.accessor.ArrayAccessor.intersection>`
+- :meth:`ArrayAccessor.difference() <piso.accessor.ArrayAccessor.difference>`
+- :meth:`ArrayAccessor.symmetric_difference() <piso.accessor.ArrayAccessor.symmetric_difference>`
 - :meth:`piso.interval.union`
 - :meth:`piso.interval.intersection`
 - :meth:`piso.interval.difference`
 - :meth:`piso.interval.symmetric_difference`
+
diff --git a/piso/__init__.py b/piso/__init__.py
index f9f67f2..c589f89 100644
--- a/piso/__init__.py
+++ b/piso/__init__.py
@@ -1,4 +1,12 @@
-from piso.intervalarray import difference, intersection, symmetric_difference, union
+from piso.intervalarray import (
+    difference,
+    intersection,
+    isdisjoint,
+    issubset,
+    issuperset,
+    symmetric_difference,
+    union,
+)
 
 
 def register_accessors():
diff --git a/piso/accessor.py b/piso/accessor.py
index cb03bf6..354c174 100644
--- a/piso/accessor.py
+++ b/piso/accessor.py
@@ -118,6 +118,29 @@ def symmetric_difference(
             return_type=return_type,
         )
 
+    @Appender(docstrings.isdisjoint_docstring, join="\n", indents=1)
+    def isdisjoint(self, *interval_arrays):
+        return intervalarray.isdisjoint(
+            self._interval_array,
+            *interval_arrays,
+        )
+
+    @Appender(docstrings.issuperset_docstring, join="\n", indents=1)
+    def issuperset(self, *interval_arrays, squeeze=False):
+        return intervalarray.issuperset(
+            self._interval_array,
+            *interval_arrays,
+            squeeze=squeeze,
+        )
+
+    @Appender(docstrings.issubset_docstring, join="\n", indents=1)
+    def issubset(self, *interval_arrays, squeeze=False):
+        return intervalarray.issubset(
+            self._interval_array,
+            *interval_arrays,
+            squeeze=squeeze,
+        )
+
 
 def _register_accessors():
     _register_accessor("piso", pd.IntervalIndex)(ArrayAccessor)
diff --git a/piso/docstrings/accessor.py b/piso/docstrings/accessor.py
index da9a779..dc6e5d8 100644
--- a/piso/docstrings/accessor.py
+++ b/piso/docstrings/accessor.py
@@ -257,6 +257,101 @@
 """
 
 
+isdisjoint_examples = """
+Examples
+-----------
+
+>>> import pandas as pd
+>>> import piso
+>>> piso.register_accessors()
+
+>>> arr1 = pd.arrays.IntervalArray.from_tuples(
+...     [(0, 3), (2, 4)],
+... )
+>>> arr2 = pd.arrays.IntervalArray.from_tuples(
+...     [(4, 7), (8, 11)],
+... )
+>>> arr3 = pd.arrays.IntervalArray.from_tuples(
+...     [(2, 4), (7, 8)],
+... )
+
+>>> arr1.piso.isdisjoint()
+False
+
+>>> arr2.piso.isdisjoint()
+True
+
+>>> arr1.piso.isdisjoint(arr2)
+True
+
+>>> arr1.piso.isdisjoint(arr3)
+False
+"""
+
+issuperset_examples = """
+Examples
+-----------
+
+>>> import pandas as pd
+>>> import piso
+>>> piso.register_accessors()
+
+>>> arr1 = pd.arrays.IntervalArray.from_tuples(
+...     [(0, 4), (3, 6), (7, 8), (10, 12)],
+... )
+>>> arr2 = pd.arrays.IntervalArray.from_tuples(
+...     [(2, 5), (7, 8)],
+... )
+>>> arr3 = pd.arrays.IntervalArray.from_tuples(
+...     [(3, 4), (10, 11)],
+... )
+
+>>> arr1.piso.issuperset(arr2)
+True
+
+>>> arr1.piso.issuperset(arr2, squeeze=False)
+array([ True])
+
+>>> arr1.piso.issuperset(arr2, arr3)
+array([ True, True])
+
+>>> arr2.piso.issuperset(arr3)
+False
+"""
+
+
+issubset_examples = """
+Examples
+-----------
+
+>>> import pandas as pd
+>>> import piso
+>>> piso.register_accessors()
+
+>>> arr1 = pd.arrays.IntervalArray.from_tuples(
+...     [(2, 5), (7, 8)],
+... )
+>>> arr2 = pd.arrays.IntervalArray.from_tuples(
+...     [(0, 4), (3, 6), (7, 8), (10, 12)],
+... )
+>>> arr3 = pd.arrays.IntervalArray.from_tuples(
+...     [(3, 4), (10, 11)],
+... )
+
+>>> arr1.piso.issubset(arr2)
+True
+
+>>> arr1.piso.issubset(arr2, squeeze=False)
+array([ True])
+
+>>> arr1.piso.issubset(arr2, arr3)
+array([ True, False])
+
+>>> arr1.piso.issubset(arr3)
+False
+"""
+
+
 def join_params(list_of_param_strings):
     return "".join(list_of_param_strings).replace("\n\n", "\n")
 
@@ -266,7 +361,7 @@ def join_params(list_of_param_strings):
     May contain zero or more arguments.
 """
 
-param_optional_args_difference = """
+param_optional_args_min_one = """
 *interval_arrays : argument list of :class:`pandas.IntervalIndex` or :class:`pandas.arrays.IntervalArray`
     Must contain at least one argument.
 """
@@ -280,8 +375,8 @@ def join_params(list_of_param_strings):
 """
 
 param_squeeze = """
-squeeze : boolean, default True
-    If True, will try to coerce the return value to a pandas.Interval.
+squeeze : boolean, default {default}
+    If True, will try to coerce the return value to a single pandas.Interval.
     If supplied, must be done so as a keyword argument.
 """
 
@@ -291,17 +386,15 @@ def join_params(list_of_param_strings):
     If supplied, must be done so as a keyword argument.
 """
 
-
 template_doc = """
-Performs a set {operation} operation.
-
 What is considered a set is determined by the number of positional arguments used, that is, determined by the
 size of *interval_arrays*.
 
-If *interval_arrays* is empty then the sets are considered to be the intervals contained in *interval_array*.
+If *interval_arrays* is empty then the sets are considered to be the intervals contained in the array object the
+accessor belongs to (an instance of :class:`pandas.IntervalIndex`, :class:`pandas.arrays.IntervalArray`).
 
 If *interval_arrays* is not empty then the sets are considered to be the elements in *interval_arrays*, in addition to the
-interval array object the accessor belongs to (an instance of :class:`pandas.IntervalIndex`, :class:`pandas.arrays.IntervalArray`).
+intervals in the array object the accessor belongs to.
 Each of these arrays is assumed to contain disjoint intervals (and satisfy the definition of a set).  Any array containing
 overlaps between intervals will be mapped to one with disjoint intervals via a union operation.
 
@@ -312,11 +405,18 @@ def join_params(list_of_param_strings):
 
 Returns
 ----------
-:class:`pandas.IntervalIndex` or :class:`pandas.arrays.IntervalArray`
+{return_type}
 
 {examples}
 """
 
+operation_template_doc = (
+    """
+Performs a set {operation} operation.
+"""
+    + template_doc
+)
+
 doc_difference_template = """
 Performs a set difference operation.
 
@@ -331,9 +431,6 @@ def join_params(list_of_param_strings):
 and the union of the sets in *interval_arrays*.  This is equivalent to iteratively applying a set difference operation with each array
 in *interval_arrays* as the second operand.
 
-Each of these array operands is assumed to contain disjoint intervals (and satisfy the definition of a set).  Any array containing
-overlaps between intervals will be mapped to one with disjoint intervals via a union operation.
-
 {extra_desc}
 Parameters
 ----------
@@ -346,18 +443,46 @@ def join_params(list_of_param_strings):
 {examples}
 """
 
+is_super_sub_set_template = """
+Indicates whether a set is a {operation} of one, or more, other sets.
+
+The array elements of *interval_arrays*, and the interval array object the accessor belongs to
+(an instance of :class:`pandas.IntervalIndex`, :class:`pandas.arrays.IntervalArray`) are considered to be the sets over which
+the operation is performed.  Each of these arrays is assumed to contain disjoint intervals (and satisfy the definition of a set).
+Any array containing overlaps between intervals will be mapped to one with disjoint intervals via a union operation.
+
+The list *interval_arrays* must contain at least one element.  The {operation} comparison is iteratively applied between
+the interval array the accessor belongs to, and each array in *interval_arrays*.  When *interval_arrays* contains multiple
+interval arrays, the return type will be a numpy array.  If it contains one interval array then the result can be coerced to
+a single boolean using the *squeeze* parameter.
+
+Parameters
+----------
+{params}
+
+Returns
+----------
+:class:`pandas.IntervalIndex` or :class:`pandas.arrays.IntervalArray`
+
+{examples}
+"""
+
+array_return_type = (
+    ":class:`pandas.IntervalIndex` or :class:`pandas.arrays.IntervalArray`"
+)
 
 union_params = join_params(
     [
         param_optional_args,
-        param_squeeze,
+        param_squeeze.format(default="False"),
         param_return_type,
     ]
 )
-union_docstring = template_doc.format(
+union_docstring = operation_template_doc.format(
     operation="union",
     extra_desc="",
     params=union_params,
+    return_type=array_return_type,
     examples=union_examples,
 )
 
@@ -365,21 +490,22 @@ def join_params(list_of_param_strings):
     [
         param_optional_args,
         param_min_overlaps,
-        param_squeeze,
+        param_squeeze.format(default="False"),
         param_return_type,
     ]
 )
-intersection_docstring = template_doc.format(
+intersection_docstring = operation_template_doc.format(
     operation="intersection",
     extra_desc="",
     params=intersection_params,
+    return_type=array_return_type,
     examples=intersection_examples,
 )
 
 difference_params = join_params(
     [
-        param_optional_args_difference,
-        param_squeeze,
+        param_optional_args_min_one,
+        param_squeeze.format(default="False"),
         param_return_type,
     ]
 )
@@ -387,6 +513,7 @@ def join_params(list_of_param_strings):
     operation="difference",
     extra_desc="",
     params=difference_params,
+    return_type=array_return_type,
     examples=difference_examples,
 )
 
@@ -395,7 +522,7 @@ def join_params(list_of_param_strings):
     [
         param_optional_args,
         param_min_overlaps,
-        param_squeeze,
+        param_squeeze.format(default="False"),
         param_return_type,
     ]
 )
@@ -404,9 +531,55 @@ def join_params(list_of_param_strings):
 The parameter *min_overlaps* in :meth:`piso.intersection`, which defines the minimum number of intervals
 in an overlap required to constitute an intersection, follows through to symmetric difference under this definition.
 """
-symmetric_difference_docstring = template_doc.format(
+symmetric_difference_docstring = operation_template_doc.format(
     operation="symmetric difference",
     extra_desc=symmetric_difference_extra_desc,
     params=symmetric_difference_params,
+    return_type=array_return_type,
     examples=symmetric_difference_examples,
 )
+
+
+isdisjoint_doc = (
+    """
+Indicates whether one, or more, sets are disjoint or not.
+"""
+    + template_doc
+)
+
+isdisjoint_params = join_params(
+    [
+        param_optional_args,
+    ]
+)
+isdisjoint_docstring = isdisjoint_doc.format(
+    extra_desc="",
+    params=isdisjoint_params,
+    return_type="boolean",
+    examples=isdisjoint_examples,
+)
+
+
+issuperset_params = join_params(
+    [
+        param_optional_args_min_one,
+        param_squeeze.format(default="True"),
+    ]
+)
+issuperset_docstring = is_super_sub_set_template.format(
+    operation="superset",
+    params=issuperset_params,
+    examples=issuperset_examples,
+)
+
+issubset_params = join_params(
+    [
+        param_optional_args_min_one,
+        param_squeeze.format(default="True"),
+    ]
+)
+issubset_docstring = is_super_sub_set_template.format(
+    operation="subset",
+    params=issubset_params,
+    examples=issubset_examples,
+)
diff --git a/piso/docstrings/interval.py b/piso/docstrings/interval.py
index 301f6ec..f326b96 100644
--- a/piso/docstrings/interval.py
+++ b/piso/docstrings/interval.py
@@ -150,8 +150,77 @@
 Length: 2, closed: right, dtype: interval[float64]
 """
 
+issuperset_examples = """
+Examples
+-----------
+
+>>> import pandas as pd
+>>> import piso.interval
+
+>>> piso.interval.issuperset(
+...    pd.Interval(1, 4),
+...    pd.Interval(2, 4),
+... )
+True
+
+>>> piso.interval.issuperset(
+...    pd.Interval(1, 4),
+...    pd.Interval(0, 3),
+... )
+False
+
+>>> piso.interval.issuperset(
+...    pd.Interval(1, 4),
+...    pd.Interval(2, 4),
+...    pd.Interval(0, 3),
+... )
+array([ True,  False])
+
+>>> piso.interval.issuperset(
+...    pd.Interval(0, 3),
+...    pd.Interval(0, 3),
+...    squeeze=False
+... )
+array([ True])
+"""
+
+
+issubset_examples = """
+Examples
+-----------
+
+>>> import pandas as pd
+>>> import piso.interval
+
+>>> piso.interval.issubset(
+...    pd.Interval(2, 4),
+...    pd.Interval(1, 4),
+... )
+True
+
+>>> piso.interval.issubset(
+...    pd.Interval(2, 4),
+...    pd.Interval(0, 3),
+... )
+False
+
+>>> piso.interval.issubset(
+...    pd.Interval(2, 4),
+...    pd.Interval(1, 4),
+...    pd.Interval(0, 3),
+... )
+array([ True,  False])
+
+>>> piso.interval.issubset(
+...    pd.Interval(1, 4),
+...    pd.Interval(1, 4),
+...    squeeze=False
+... )
+array([ True])
+"""
+
 template_doc = """
-Performs the {operation} of two pandas.Intervals
+Performs the {operation} of two :class:`pandas.Interval`
 
 Parameters
 ----------
@@ -160,7 +229,7 @@
 interval2 : pandas.Interval
     the second operand
 squeeze : boolean, default True
-    If True, will try to coerce the return value to a pandas.Interval
+    If True, will try to coerce the return value to a :class:`pandas.Interval`
 
 Returns
 ----------
@@ -169,6 +238,7 @@
 {examples}
 """
 
+
 union_docstring = template_doc.format(operation="union", examples=union_examples)
 intersection_docstring = template_doc.format(
     operation="intersection", examples=intersection_examples
@@ -179,3 +249,33 @@
 symmetric_difference_docstring = template_doc.format(
     operation="symmetric difference", examples=symmetric_difference_examples
 )
+
+
+is_sub_super_doc = """
+Indicates whether one :class:`pandas.Interval` is a {operation} of one, or more, others.
+
+Parameters
+----------
+interval : :class:`pandas.Interval`
+    An interval, against which all other intervals belonging to *intervals* are compared.
+*intervals : argument list of :class:`pandas.Interval`
+    Must contain at least one argument.
+squeeze : boolean, default True
+    If True, will try to coerce the return value to a single boolean
+
+Returns
+----------
+boolean, or :class:`numpy.ndarray` of booleans
+
+{examples}
+"""
+
+issuperset_docstring = is_sub_super_doc.format(
+    operation="superset",
+    examples=issuperset_examples,
+)
+
+issubset_docstring = is_sub_super_doc.format(
+    operation="subset",
+    examples=issubset_examples,
+)
diff --git a/piso/docstrings/intervalarray.py b/piso/docstrings/intervalarray.py
index 09c6371..92e5f36 100644
--- a/piso/docstrings/intervalarray.py
+++ b/piso/docstrings/intervalarray.py
@@ -241,6 +241,99 @@
 """
 
 
+isdisjoint_examples = """
+Examples
+-----------
+
+>>> import pandas as pd
+>>> import piso
+
+>>> arr1 = pd.arrays.IntervalArray.from_tuples(
+...     [(0, 3), (2, 4)],
+... )
+>>> arr2 = pd.arrays.IntervalArray.from_tuples(
+...     [(4, 7), (8, 11)],
+... )
+>>> arr3 = pd.arrays.IntervalArray.from_tuples(
+...     [(2, 4), (7, 8)],
+... )
+
+>>> piso.isdisjoint(arr1)
+False
+
+>>> piso.isdisjoint(arr2)
+True
+
+>>> piso.isdisjoint(arr1, arr2)
+True
+
+>>> piso.isdisjoint(arr1, arr3)
+False
+"""
+
+
+issuperset_examples = """
+Examples
+-----------
+
+>>> import pandas as pd
+>>> import piso
+
+>>> arr1 = pd.arrays.IntervalArray.from_tuples(
+...     [(0, 4), (3, 6), (7, 8), (10, 12)],
+... )
+>>> arr2 = pd.arrays.IntervalArray.from_tuples(
+...     [(2, 5), (7, 8)],
+... )
+>>> arr3 = pd.arrays.IntervalArray.from_tuples(
+...     [(3, 4), (10, 11)],
+... )
+
+>>> piso.issuperset(arr1, arr2)
+True
+
+>>> piso.issuperset(arr1, arr2, squeeze=False)
+array([ True])
+
+>>> piso.issuperset(arr1, arr2, arr3)
+array([ True, True])
+
+>>> piso.issuperset(arr2, arr3)
+False
+"""
+
+
+issubset_examples = """
+Examples
+-----------
+
+>>> import pandas as pd
+>>> import piso
+
+>>> arr1 = pd.arrays.IntervalArray.from_tuples(
+...     [(2, 5), (7, 8)],
+... )
+>>> arr2 = pd.arrays.IntervalArray.from_tuples(
+...     [(0, 4), (3, 6), (7, 8), (10, 12)],
+... )
+>>> arr3 = pd.arrays.IntervalArray.from_tuples(
+...     [(3, 4), (10, 11)],
+... )
+
+>>> piso.issubset(arr1, arr2)
+True
+
+>>> piso.issubset(arr1, arr2, squeeze=False)
+array([ True])
+
+>>> piso.issubset(arr1, arr2, arr3)
+array([ True, False])
+
+>>> piso.issubset(arr1, arr3)
+False
+"""
+
+
 def join_params(list_of_param_strings):
     return "".join(list_of_param_strings).replace("\n\n", "\n")
 
@@ -250,12 +343,22 @@ def join_params(list_of_param_strings):
     The first (and possibly only) operand to the {operation} operation.
 """
 
+param_interval_array_non_optional = """
+interval_array : :class:`pandas.IntervalIndex` or :class:`pandas.arrays.IntervalArray`
+    The first operand to the {operation} operation.
+"""
+
+param_interval_sub_super_set = """
+interval_array : :class:`pandas.IntervalIndex` or :class:`pandas.arrays.IntervalArray`
+    The first operand to which all others are compared operation.
+"""
+
 param_optional_args = """
 *interval_arrays : argument list of :class:`pandas.IntervalIndex` or :class:`pandas.arrays.IntervalArray`
     May contain zero or more arguments.
 """
 
-param_optional_args_difference = """
+param_optional_args_min_one = """
 *interval_arrays : argument list of :class:`pandas.IntervalIndex` or :class:`pandas.arrays.IntervalArray`
     Must contain at least one argument.
 """
@@ -269,8 +372,8 @@ def join_params(list_of_param_strings):
 """
 
 param_squeeze = """
-squeeze : boolean, default True
-    If True, will try to coerce the return value to a pandas.Interval.
+squeeze : boolean, default {default}
+    If True, will try to coerce the return value to a single pandas.Interval.
     If supplied, must be done so as a keyword argument.
 """
 
@@ -282,8 +385,6 @@ def join_params(list_of_param_strings):
 
 
 template_doc = """
-Performs a set {operation} operation.
-
 What is considered a set is determined by the number of positional arguments used, that is, determined by the
 size of *interval_arrays*.
 
@@ -300,11 +401,20 @@ def join_params(list_of_param_strings):
 
 Returns
 ----------
-:class:`pandas.IntervalIndex` or :class:`pandas.arrays.IntervalArray`
+{return_type}
 
 {examples}
 """
 
+
+operation_template_doc = (
+    """
+Performs a set {operation} operation.
+"""
+    + template_doc
+)
+
+
 doc_difference_template = """
 Performs a set difference operation.
 
@@ -317,9 +427,6 @@ def join_params(list_of_param_strings):
 multiple elements then the result is the set difference between *interval_array* and the union of the sets in *interval_arrays*.
 This is equivalent to iteratively applying a set difference operation with each array in *interval_arrays* as the second operand.
 
-Each of these array operands is assumed to contain disjoint intervals (and satisfy the definition of a set).  Any array containing
-overlaps between intervals will be mapped to one with disjoint intervals via a union operation.
-
 {extra_desc}
 Parameters
 ----------
@@ -332,19 +439,48 @@ def join_params(list_of_param_strings):
 {examples}
 """
 
+doc_is_sub_super_set_template = """
+Indicates whether a set is a {operation} of one, or more, other sets.
+
+The argument *interval_array* and the array elements of *interval_arrays* are all considered to be the sets for the purposes
+of this set method.  Each of these arrays is assumed to contain disjoint intervals (and satisfy the definition of a set).
+Any array containing overlaps between intervals will be mapped to one with disjoint intervals via a union operation.
+
+The list *interval_arrays* must contain at least one element.  The {operation} comparison is iteratively applied between
+*interval_array* and each array in *interval_arrays*.  When *interval_arrays* contains multiple interval arrays, the return
+type will be a numpy array.  If it contains one interval array then the result can be coerced to a single boolean using the
+*squeeze* parameter.
+
+{extra_desc}
+Parameters
+----------
+{params}
+
+Returns
+----------
+boolean, or :class:`numpy.ndarray` of boolean
+
+{examples}
+"""
+
+
+array_return_type = (
+    ":class:`pandas.IntervalIndex` or :class:`pandas.arrays.IntervalArray`"
+)
 
 union_params = join_params(
     [
         param_interval_array.format(operation="union"),
         param_optional_args,
-        param_squeeze,
+        param_squeeze.format(default="False"),
         param_return_type,
     ]
 )
-union_docstring = template_doc.format(
+union_docstring = operation_template_doc.format(
     operation="union",
     extra_desc="",
     params=union_params,
+    return_type=array_return_type,
     examples=union_examples,
 )
 
@@ -353,22 +489,23 @@ def join_params(list_of_param_strings):
         param_interval_array.format(operation="intersection"),
         param_optional_args,
         param_min_overlaps,
-        param_squeeze,
+        param_squeeze.format(default="False"),
         param_return_type,
     ]
 )
-intersection_docstring = template_doc.format(
+intersection_docstring = operation_template_doc.format(
     operation="intersection",
     extra_desc="",
     params=intersection_params,
+    return_type=array_return_type,
     examples=intersection_examples,
 )
 
 difference_params = join_params(
     [
-        param_interval_array.format(operation="difference"),
-        param_optional_args_difference,
-        param_squeeze,
+        param_interval_array_non_optional.format(operation="difference"),
+        param_optional_args_min_one,
+        param_squeeze.format(default="False"),
         param_return_type,
     ]
 )
@@ -376,6 +513,7 @@ def join_params(list_of_param_strings):
     operation="difference",
     extra_desc="",
     params=difference_params,
+    return_type=array_return_type,
     examples=difference_examples,
 )
 
@@ -385,7 +523,7 @@ def join_params(list_of_param_strings):
         param_interval_array.format(operation="symmetric difference"),
         param_optional_args,
         param_min_overlaps,
-        param_squeeze,
+        param_squeeze.format(default="False"),
         param_return_type,
     ]
 )
@@ -394,9 +532,61 @@ def join_params(list_of_param_strings):
 The parameter *min_overlaps* in :meth:`piso.intersection`, which defines the minimum number of intervals
 in an overlap required to constitute an intersection, follows through to symmetric difference under this definition.
 """
-symmetric_difference_docstring = template_doc.format(
+symmetric_difference_docstring = operation_template_doc.format(
     operation="symmetric difference",
     extra_desc=symmetric_difference_extra_desc,
     params=symmetric_difference_params,
+    return_type=array_return_type,
     examples=symmetric_difference_examples,
 )
+
+
+isdisjoint_doc = (
+    """
+Indicates whether one, or more, sets are disjoint or not.
+"""
+    + template_doc
+)
+
+isdisjoint_params = join_params(
+    [
+        param_interval_array.format(operation="isdisjoint"),
+        param_optional_args,
+    ]
+)
+isdisjoint_docstring = isdisjoint_doc.format(
+    extra_desc="",
+    params=isdisjoint_params,
+    return_type="boolean",
+    examples=isdisjoint_examples,
+)
+
+
+issuperset_params = join_params(
+    [
+        param_interval_sub_super_set,
+        param_optional_args_min_one,
+        param_squeeze.format(default="True"),
+    ]
+)
+issuperset_docstring = doc_is_sub_super_set_template.format(
+    operation="superset",
+    extra_desc="",
+    params=issuperset_params,
+    examples=issuperset_examples,
+)
+
+
+issubset_params = join_params(
+    [
+        param_interval_sub_super_set,
+        param_optional_args_min_one,
+        param_squeeze.format(default="True"),
+    ]
+)
+issubset_docstring = doc_is_sub_super_set_template.format(
+    operation="subset",
+    extra_desc="",
+    params=issubset_params,
+    examples=issubset_examples,
+)
diff --git a/piso/interval.py b/piso/interval.py
index 4ac94db..619be29 100644
--- a/piso/interval.py
+++ b/piso/interval.py
@@ -1,3 +1,4 @@
+import numpy as np
 import pandas as pd
 
 import piso.docstrings.interval as docstrings
@@ -109,3 +110,31 @@ def symmetric_difference(interval1, interval2, squeeze=True):
             closed=interval1.closed,
         )
     return result
+
+
+def _make_is_sub_or_superset(which, docstring):
+
+    left_bound_comparator = {"super": np.less_equal, "sub": np.greater_equal}[which]
+    right_bound_comparator = {"super": np.greater_equal, "sub": np.less_equal}[which]
+
+    @Appender(docstring, join="\n", indents=1)
+    def func(interval, *intervals, squeeze=True):
+        assert intervals
+        lefts = np.array([i.left for i in intervals])
+        rights = np.array([i.right for i in intervals])
+
+        result = np.logical_and(
+            left_bound_comparator(interval.left, lefts),
+            right_bound_comparator(interval.right, rights),
+        )
+
+        if len(result) == 1 and squeeze:
+            result = result[0]
+
+        return result
+
+    return func
+
+
+issuperset = _make_is_sub_or_superset("super", docstrings.issuperset_docstring)
+issubset = _make_is_sub_or_superset("sub", docstrings.issubset_docstring)
diff --git a/piso/intervalarray.py b/piso/intervalarray.py
index 400ccaa..3c635aa 100644
--- a/piso/intervalarray.py
+++ b/piso/intervalarray.py
@@ -1,3 +1,4 @@
+import numpy as np
 import pandas as pd
 import staircase as sc
 
@@ -103,3 +104,49 @@ def symmetric_difference(
     if squeeze and len(result) == 1:
         result = result[0]
     return result
+
+
+@Appender(docstrings.isdisjoint_docstring, join="\n", indents=1)
+def isdisjoint(interval_array, *interval_arrays):
+    _validate_array_of_intervals_arrays(interval_array, *interval_arrays)
+    if interval_arrays:
+        stairs = _make_stairs(interval_array, *interval_arrays)
+        result = stairs.max() <= 1
+    elif len(interval_array) == 0:
+        result = True
+    else:
+        arr = np.stack([interval_array.left.values, interval_array.right.values])
+        arr = arr[arr[:, 0].argsort()]
+        result = np.all(arr[0, 1:] >= arr[1, :-1])
+    return result
+
+
+def _create_is_super_or_sub(which, docstring):
+
+    comparator_func = {"superset": sc.Stairs.ge, "subset": sc.Stairs.le}[which]
+
+    @Appender(docstring, join="\n", indents=1)
+    def func(interval_array, *interval_arrays, squeeze=True):
+        _validate_array_of_intervals_arrays(interval_array, *interval_arrays)
+        assert interval_arrays
+        stepfunction = _interval_x_to_stairs(interval_array).make_boolean()
+
+        def _comp(ia):
+            return bool(
+                comparator_func(
+                    stepfunction,
+                    _interval_x_to_stairs(ia).make_boolean(),
+                )
+            )
+
+        result = np.array([_comp(ia) for ia in interval_arrays])
+
+        if squeeze and len(result) == 1:
+            result = result[0]
+        return result
+
+    return func
+
+
+issuperset = _create_is_super_or_sub("superset", docstrings.issuperset_docstring)
+issubset = _create_is_super_or_sub("subset", docstrings.issubset_docstring)
diff --git a/poetry.lock b/poetry.lock
index 1f95306..b1013b5 100644
--- a/poetry.lock
+++ b/poetry.lock
@@ -196,7 +196,7 @@ python-versions = ">=2.7, !=3.0.*, !=3.1.*, !=3.2.*, !=3.3.*, !=3.4.*"
 
 [[package]]
 name = "coverage"
-version = "6.0.1"
+version = "6.0.2"
 description = "Code coverage measurement for Python"
 category = "dev"
 optional = false
@@ -1221,7 +1221,7 @@ test = ["pytest"]
 
 [[package]]
 name = "staircase"
-version = "2.0.3"
+version = "2.0.4"
 description = "A data analysis package based on modelling and manipulation of mathematical step functions. Strongly aligned with pandas."
 category = "main"
 optional = false
@@ -1407,7 +1407,7 @@ codecov = []
 [metadata]
 lock-version = "1.1"
 python-versions = "^3.6.1"
-content-hash = "0c02826b5a19e9649cfa35dc3509171da804c1c04f713da7ebaeb7846010e98f"
+content-hash = "0a47702bf0b60eb123c87a8953108f3b390be1ada8017fe850f7af71b67e1836"
 
 [metadata.files]
 alabaster = [
@@ -1531,39 +1531,39 @@ colorama = [
     {file = "colorama-0.4.4.tar.gz", hash = "sha256:5941b2b48a20143d2267e95b1c2a7603ce057ee39fd88e7329b0c292aa16869b"},
 ]
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+    {file = "coverage-6.0.2-cp38-cp38-win32.whl", hash = "sha256:a1b73c7c4d2a42b9d37dd43199c5711d91424ff3c6c22681bc132db4a4afec6f"},
+    {file = "coverage-6.0.2-cp38-cp38-win_amd64.whl", hash = "sha256:1db67c497688fd4ba85b373b37cc52c50d437fd7267520ecd77bddbd89ea22c9"},
+    {file = "coverage-6.0.2-cp39-cp39-macosx_10_9_x86_64.whl", hash = "sha256:f2f184bf38e74f152eed7f87e345b51f3ab0b703842f447c22efe35e59942c24"},
+    {file = "coverage-6.0.2-cp39-cp39-manylinux_2_17_aarch64.manylinux2014_aarch64.whl", hash = "sha256:cd1cf1deb3d5544bd942356364a2fdc8959bad2b6cf6eb17f47d301ea34ae822"},
+    {file = "coverage-6.0.2-cp39-cp39-manylinux_2_5_i686.manylinux1_i686.manylinux_2_12_i686.manylinux2010_i686.whl", hash = "sha256:ad9b8c1206ae41d46ec7380b78ba735ebb77758a650643e841dd3894966c31d0"},
+    {file = "coverage-6.0.2-cp39-cp39-manylinux_2_5_x86_64.manylinux1_x86_64.manylinux_2_12_x86_64.manylinux2010_x86_64.whl", hash = "sha256:381d773d896cc7f8ba4ff3b92dee4ed740fb88dfe33b6e42efc5e8ab6dfa1cfe"},
+    {file = "coverage-6.0.2-cp39-cp39-win32.whl", hash = "sha256:424c44f65e8be58b54e2b0bd1515e434b940679624b1b72726147cfc6a9fc7ce"},
+    {file = "coverage-6.0.2-cp39-cp39-win_amd64.whl", hash = "sha256:abbff240f77347d17306d3201e14431519bf64495648ca5a49571f988f88dee9"},
+    {file = "coverage-6.0.2-pp36-none-any.whl", hash = "sha256:7092eab374346121805fb637572483270324407bf150c30a3b161fc0c4ca5164"},
+    {file = "coverage-6.0.2-pp37-none-any.whl", hash = "sha256:30922626ce6f7a5a30bdba984ad21021529d3d05a68b4f71ea3b16bda35b8895"},
+    {file = "coverage-6.0.2.tar.gz", hash = "sha256:6807947a09510dc31fa86f43595bf3a14017cd60bf633cc746d52141bfa6b149"},
 ]
 cycler = [
     {file = "cycler-0.10.0-py2.py3-none-any.whl", hash = "sha256:1d8a5ae1ff6c5cf9b93e8811e581232ad8920aeec647c37316ceac982b08cb2d"},
@@ -2218,8 +2218,8 @@ sphinxcontrib-serializinghtml = [
     {file = "sphinxcontrib_serializinghtml-1.1.5-py2.py3-none-any.whl", hash = "sha256:352a9a00ae864471d3a7ead8d7d79f5fc0b57e8b3f95e9867eb9eb28999b92fd"},
 ]
 staircase = [
-    {file = "staircase-2.0.3-py3-none-any.whl", hash = "sha256:d856f8d37ef789309ca575053457b9b52f77244ac1a5338af811c9ede982da50"},
-    {file = "staircase-2.0.3.tar.gz", hash = "sha256:e0640f4813574b742a80a054cce25a00895571f8f43e4b7a52a58a53944b7872"},
+    {file = "staircase-2.0.4-py3-none-any.whl", hash = "sha256:c45291e8c91c3faf485790b483563580098c55f2c2f586ac7b41f05cbd27d8ac"},
+    {file = "staircase-2.0.4.tar.gz", hash = "sha256:25e019e3d3d930153bd2c5381029198e865db0b0732fdda6f85550930ffee14c"},
 ]
 terminado = [
     {file = "terminado-0.12.1-py3-none-any.whl", hash = "sha256:09fdde344324a1c9c6e610ee4ca165c4bb7f5bbf982fceeeb38998a988ef8452"},
diff --git a/pyproject.toml b/pyproject.toml
index ae52f38..7e8fbbd 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -6,7 +6,7 @@ build-backend = "poetry.masonry.api"
 
 [tool.poetry]
 name = "piso"
-version = "0.1.0"
+version = "0.2.0"
 description = "Pandas Interval Set Operations: methods for set operations for pandas' Interval, IntervalArray and IntervalIndex"
 readme = "README.md"
 authors = ["Riley Clement <venaturum@gmail.com>"]
@@ -41,7 +41,7 @@ classifiers=[
 
 [tool.poetry.dependencies]
 python = "^3.6.1"
-staircase = "^2.0.3"
+staircase = "^2.0.4"
 pandas = "^1"
 
 
diff --git a/tests/test_interval.py b/tests/test_interval.py
index b0fda74..2927308 100644
--- a/tests/test_interval.py
+++ b/tests/test_interval.py
@@ -1,3 +1,6 @@
+import operator
+
+import numpy as np
 import pandas as pd
 import pytest
 
@@ -624,3 +627,47 @@ def test_symmetric_difference_closed_value_error(closed_values):
     )
     with pytest.raises(ClosedValueError):
         piso_interval.symmetric_difference(*intervals)
+
+
+@pytest.mark.parametrize(
+    "tuples, squeeze, expected",
+    [
+        ([(1, 2), (1, 2)], True, True),
+        ([(1, 3), (0, 2)], True, False),
+        ([(1, 3), (1, 2), (0, 1)], True, np.array([True, False])),
+        ([(1, 2), (1, 2)], False, np.array([True])),
+        ([(1, 3), (0, 2)], False, np.array([False])),
+        ([(1, 3), (1, 2), (0, 1)], False, np.array([True, False])),
+    ],
+)
+@pytest.mark.parametrize(
+    "closed",
+    ["left", "right"],
+)
+def test_issuperset(tuples, squeeze, expected, closed):
+    intervals = [pd.Interval(*i, closed=closed) for i in tuples]
+    result = piso_interval.issuperset(*intervals, squeeze=squeeze)
+    equal_op = np.array_equal if isinstance(expected, np.ndarray) else operator.eq
+    assert equal_op(result, expected)
+
+
+@pytest.mark.parametrize(
+    "tuples, squeeze, expected",
+    [
+        ([(1, 2), (1, 2)], True, True),
+        ([(1, 3), (0, 2)], True, False),
+        ([(1, 3), (1, 4), (0, 1)], True, np.array([True, False])),
+        ([(1, 2), (1, 2)], False, np.array([True])),
+        ([(1, 3), (0, 2)], False, np.array([False])),
+        ([(1, 3), (1, 4), (0, 1)], False, np.array([True, False])),
+    ],
+)
+@pytest.mark.parametrize(
+    "closed",
+    ["left", "right"],
+)
+def test_issubset(tuples, squeeze, expected, closed):
+    intervals = [pd.Interval(*i, closed=closed) for i in tuples]
+    result = piso_interval.issubset(*intervals, squeeze=squeeze)
+    equal_op = np.array_equal if isinstance(expected, np.ndarray) else operator.eq
+    assert equal_op(result, expected)
diff --git a/tests/test_multiple_interval_array.py b/tests/test_multiple_interval_array.py
index 74ed169..24dc187 100644
--- a/tests/test_multiple_interval_array.py
+++ b/tests/test_multiple_interval_array.py
@@ -1,3 +1,6 @@
+import operator
+
+import numpy as np
 import pandas as pd
 import pytest
 
@@ -14,6 +17,9 @@ def get_accessor_method(self, function):
         piso_intervalarray.intersection: self.piso.intersection,
         piso_intervalarray.difference: self.piso.difference,
         piso_intervalarray.symmetric_difference: self.piso.symmetric_difference,
+        piso_intervalarray.isdisjoint: self.piso.isdisjoint,
+        piso_intervalarray.issuperset: self.piso.issuperset,
+        piso_intervalarray.issubset: self.piso.issubset,
     }[function]
 
 
@@ -23,6 +29,9 @@ def get_package_method(function):
         piso_intervalarray.intersection: piso.intersection,
         piso_intervalarray.symmetric_difference: piso.symmetric_difference,
         piso_intervalarray.difference: piso.difference,
+        piso_intervalarray.isdisjoint: piso.isdisjoint,
+        piso_intervalarray.issuperset: piso.issuperset,
+        piso_intervalarray.issubset: piso.issubset,
     }[function]
 
 
@@ -429,3 +438,136 @@ def test_difference_4(closed, interval_index, return_type, how):
         expected,
         interval_index,
     )
+
+
+def map_to_dates(interval_array, date_type):
+    def make_date(x):
+        ts = pd.Timestamp(f"2021-10-{x}")
+        if date_type == "numpy":
+            return ts.to_numpy()
+        if date_type == "datetime":
+            return ts.to_pydatetime()
+        if date_type == "timedelta":
+            return ts - pd.Timestamp("2021-10-1")
+        return ts
+
+    return interval_array.from_arrays(
+        interval_array.left.map(make_date),
+        interval_array.right.map(make_date),
+    )
+
+
+def make_ia_from_tuples(interval_index, tuples, closed):
+    klass = pd.IntervalIndex if interval_index else pd.arrays.IntervalArray
+    return klass.from_tuples(tuples, closed=closed)
+
+
+@pytest.mark.parametrize(
+    "interval_index",
+    [True, False],
+)
+@pytest.mark.parametrize(
+    "tuples, expected",
+    [
+        ([], True),
+        ([(1, 3)], True),
+        ([(3, 11)], False),
+        ([(1, 2), (2, 3)], True),
+        ([(1, 2), (1, 3)], True),
+        ([(1, 3), (7, 9)], False),
+        ([(1, 5), (6, 7)], False),
+        ([(1, 2), (6, 7), (9, 10)], False),
+    ],
+)
+@pytest.mark.parametrize(
+    "closed",
+    ["left", "right"],
+)
+@pytest.mark.parametrize(
+    "date_type",
+    ["timestamp", "numpy", "datetime", "timedelta", None],
+)
+@pytest.mark.parametrize(
+    "how",
+    ["supplied", "accessor", "package"],
+)
+def test_isdisjoint(interval_index, tuples, expected, closed, date_type, how):
+    # all intervals are compared to ia3
+    ia3 = make_ia3(interval_index, closed)  # intervals = (3,4), (8,11)
+    ia3 = map_to_dates(ia3, date_type)
+    interval_array = make_ia_from_tuples(interval_index, tuples, closed)
+    interval_array = map_to_dates(interval_array, date_type)
+    result = perform_op(
+        ia3, interval_array, how=how, function=piso_intervalarray.isdisjoint
+    )
+    assert result == expected
+
+
+@pytest.mark.parametrize(
+    "interval_index",
+    [True, False],
+)
+@pytest.mark.parametrize(
+    "ia_makers, squeeze, expected",
+    [
+        ([make_ia1, make_ia2], True, True),
+        ([make_ia1, make_ia3], True, False),
+        ([make_ia1, make_ia2, make_ia3], True, np.array([True, False])),
+        ([make_ia1, make_ia2], False, np.array([True])),
+        ([make_ia1, make_ia3], False, np.array([False])),
+        ([make_ia1, make_ia2, make_ia3], False, np.array([True, False])),
+    ],
+)
+@pytest.mark.parametrize(
+    "closed",
+    ["left", "right"],
+)
+@pytest.mark.parametrize(
+    "how",
+    ["supplied", "accessor", "package"],
+)
+def test_issuperset(interval_index, ia_makers, squeeze, expected, closed, how):
+    ias = [make_ia(interval_index, closed) for make_ia in ia_makers]
+    result = perform_op(
+        *ias,
+        how=how,
+        function=piso_intervalarray.issuperset,
+        squeeze=squeeze,
+    )
+    equal_op = np.array_equal if isinstance(expected, np.ndarray) else operator.eq
+    assert equal_op(result, expected)
+
+
+@pytest.mark.parametrize(
+    "interval_index",
+    [True, False],
+)
+@pytest.mark.parametrize(
+    "ia_makers, squeeze, expected",
+    [
+        ([make_ia2, make_ia1], True, True),
+        ([make_ia3, make_ia1], True, False),
+        ([make_ia2, make_ia1, make_ia3], True, np.array([True, False])),
+        ([make_ia2, make_ia1], False, np.array([True])),
+        ([make_ia3, make_ia1], False, np.array([False])),
+        ([make_ia2, make_ia1, make_ia3], False, np.array([True, False])),
+    ],
+)
+@pytest.mark.parametrize(
+    "closed",
+    ["left", "right"],
+)
+@pytest.mark.parametrize(
+    "how",
+    ["supplied", "accessor", "package"],
+)
+def test_issubset(interval_index, ia_makers, squeeze, expected, closed, how):
+    ias = [make_ia(interval_index, closed) for make_ia in ia_makers]
+    result = perform_op(
+        *ias,
+        how=how,
+        function=piso_intervalarray.issubset,
+        squeeze=squeeze,
+    )
+    equal_op = np.array_equal if isinstance(expected, np.ndarray) else operator.eq
+    assert equal_op(result, expected)
diff --git a/tests/test_single_interval_array.py b/tests/test_single_interval_array.py
index 3d7875e..bdb91dd 100644
--- a/tests/test_single_interval_array.py
+++ b/tests/test_single_interval_array.py
@@ -13,6 +13,9 @@ def get_accessor_method(self, function):
         piso_intervalarray.union: self.piso.union,
         piso_intervalarray.intersection: self.piso.intersection,
         piso_intervalarray.symmetric_difference: self.piso.symmetric_difference,
+        piso_intervalarray.isdisjoint: self.piso.isdisjoint,
+        piso_intervalarray.issuperset: self.piso.issuperset,
+        piso_intervalarray.issubset: self.piso.issubset,
     }[function]
 
 
@@ -21,6 +24,9 @@ def get_package_method(function):
         piso_intervalarray.union: piso.union,
         piso_intervalarray.intersection: piso.intersection,
         piso_intervalarray.symmetric_difference: piso.symmetric_difference,
+        piso_intervalarray.isdisjoint: piso_intervalarray.isdisjoint,
+        piso_intervalarray.issuperset: piso.issuperset,
+        piso_intervalarray.issubset: piso.issubset,
     }[function]
 
 
@@ -65,6 +71,11 @@ def make_ia3(interval_index, closed):
     return ia3
 
 
+def make_ia_from_tuples(interval_index, tuples, closed):
+    klass = pd.IntervalIndex if interval_index else pd.arrays.IntervalArray
+    return klass.from_tuples(tuples, closed=closed)
+
+
 def assert_interval_array_equal(interval_array, expected, interval_index):
     if interval_index:
         interval_array = interval_array.values
@@ -418,3 +429,58 @@ def test_symmetric_difference_min_overlaps_all_2(
         expected,
         interval_index,
     )
+
+
+def map_to_dates(interval_array, date_type):
+    def make_date(x):
+        ts = pd.Timestamp(f"2021-10-{x}")
+        if date_type == "numpy":
+            return ts.to_numpy()
+        if date_type == "datetime":
+            return ts.to_pydatetime()
+        if date_type == "timedelta":
+            return ts - pd.Timestamp("2021-10-1")
+        return ts
+
+    return interval_array.from_arrays(
+        interval_array.left.map(make_date),
+        interval_array.right.map(make_date),
+    )
+
+
+@pytest.mark.parametrize(
+    "interval_index",
+    [True, False],
+)
+@pytest.mark.parametrize(
+    "tuples, expected",
+    [
+        ([], True),
+        ([(1, 2), (2, 3)], True),
+        ([(1, 2), (3, 4)], True),
+        ([(1, 3), (2, 4)], False),
+        ([(1, 4), (2, 3)], False),
+        ([(1, 2), (2, 3), (3, 4)], True),
+        ([(1, 2), (3, 4), (5, 6)], True),
+        ([(1, 3), (2, 4), (5, 6)], False),
+        ([(1, 4), (2, 3), (5, 6)], False),
+    ],
+)
+@pytest.mark.parametrize(
+    "closed",
+    ["left", "right"],
+)
+@pytest.mark.parametrize(
+    "date_type",
+    ["timestamp", "numpy", "datetime", "timedelta", None],
+)
+@pytest.mark.parametrize(
+    "how",
+    ["supplied", "accessor", "package"],
+)
+def test_isdisjoint(interval_index, tuples, expected, closed, date_type, how):
+
+    interval_array = make_ia_from_tuples(interval_index, tuples, closed)
+    interval_array = map_to_dates(interval_array, date_type)
+    result = perform_op(interval_array, how=how, function=piso_intervalarray.isdisjoint)
+    assert result == expected