We define two sets a and b

>>> a = {1, 2, 2, 3, 4}
>>> b = {3, 3, 4, 4, 5}

NOTE: {1} creates a set of one element, but {} creates an empty dict. The correct way to create an empty set is set().

Intersection

a.intersection(b) returns a new set with elements present in both a and b

>>> a.intersection(b)
{3, 4}

Union

a.union(b) returns a new set with elements present in either a and b

>>> a.union(b)
{1, 2, 3, 4, 5}

Difference

a.difference(b) returns a new set with elements present in a but not in b

>>> a.difference(b)
{1, 2}
>>> b.difference(a)
{5}

Symmetric Difference

a.symmetric_difference(b) returns a new set with elements present in either a or b but not in both

>>> a.symmetric_difference(b)
{1, 2, 5}
>>> b.symmetric_difference(a)
{1, 2, 5}

NOTE: a.symmetric_difference(b) == b.symmetric_difference(a)

Subset and superset

c.issubset(a) tests whether each element of c is in a.

a.issuperset(c) tests whether each element of c is in a.

>>> c = {1, 2}
>>> c.issubset(a)
True
>>> a.issuperset(c)
True

The latter operations have equivalent operators as shown below:

|Method                      |Operator        |
|––––––––––––––|––––––––|
|`a.intersection(b)`         | `a & b`        |
|`a.union(b)`                | `a`|`b` |
|`a.difference(b)`           | `a - b`        |
|`a.symmetric_difference(b)` | `a ^ b`        |
|`a.issubset(b)`             | `a <= b`       |
|`a.issuperset(b)`           | `a >= b`       |

Disjoint sets

Sets a and d are disjoint if no element in a is also in d and vice versa.

>>> d = {5, 6}
>>> a.isdisjoint(b) # {2, 3, 4} are in both sets
False
>>> a.isdisjoint(d)
True

# This is an equivalent check, but less efficient
>>> len(a & d) == 0
True

# This is even less efficient
>>> a & d == set()
True

Testing membership

The builtin in keyword searches for occurances

>>> 1 in a
True
>>> 6 in a
False

Length

The builtin len() function returns the number of elements in the set

>>> len(a)
4
>>> len(b)
3