Set notation

∈

Is an element of / belongs to. Example: 3 ∈ {1, 2, 3}

∉

Is not an element of / does not belong to. Example: 4 ∉ {1, 2, 3}

⊆

Is a subset of (possibly equal). Every element of A is also in B.

⊊

Is a proper subset of. Every element of A is in B, but A ≠ B.

∪

Union — elements in A OR B (or both).

∩

Intersection — elements in BOTH A AND B.

∖

Set difference — elements in A but NOT in B.

Aᶜ

Complement of A — everything in the universal set that is not in A.

∅

Empty set — a set containing no elements.

P(A)

Power set of A — the set containing all possible subsets of A.

A × B

Cartesian product — all ordered pairs (a, b) where a ∈ A and b ∈ B.

∀

For all / for every.

∃

There exists / there is at least one.

∃!

There exists exactly one.

∧

Logical AND — both statements must be true.

∨

Logical OR — at least one statement must be true.

¬

Logical NOT — negates a statement.

| or :

Such that — used in set-builder notation.