12.7 Set Operators

Sets support real mathematical set operations directly as operators — the same conceptual operations from set theory, applied to Python collections.

| (Union)

Everything in either set (or both) — combines all unique elements.

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

& (Intersection)

Only elements in both sets.

>>> a & b
{2, 3}

- (Difference)

Elements in the first set but not the second — order matters here, unlike union/intersection.

>>> a - b
{1}

^ (Symmetric Difference)

Elements in exactly one of the two sets (i.e. everything except the overlap).

>>> a ^ b
{1, 4}

Membership (in, not in)

The operation sets are famous for — O(1) average, versus O(n) for the same check on a list (see 10.6 List Operators).

>>> 2 in a, 5 not in a
(True, True)

Quick Interview Answer

“Sets support four operators straight out of set theory: | for union (everything in either), & for intersection (only what’s in both), - for difference (in the first but not the second — order matters here, unlike the other three), and ^ for symmetric difference (in exactly one, not both). Each has a method equivalent too (see 12.8 Set Methods), useful when chaining or passing as a callback. And in/not in membership testing is the operation sets exist for — O(1) average via a direct hash lookup, versus O(n) for the same check on a list.”

Common Mistakes

• Assuming - is symmetric like | and & — a - b and b - a are generally different sets; only ^ is order-independent for “what differs.”
• Forgetting that |, &, and - all build a new set rather than mutating either operand.
• Reaching for a list and a manual loop to find common or missing elements between two collections, instead of converting to sets and using & or - directly (see 12.14 Common Algorithms).