Discrete Math Symbols

List of all Discrete Math Symbols

∈

“element of”

3 ∈ {1, 2, 3}

3 is in the set

∉

“not element of”

4 ∉ {1, 2, 3}

4 is not in the set

⊂

“proper subset of”

{1,2} ⊂ {1,2,3}

Left set is part of the right set

⊆

"subset of or equal to"

A ⊆ A

A includes all elements of itself

⊃

“proper superset of"

{1,2,3} ⊃ {1,2}

Reverse of subset

∪

union

A ∪ B

All elements in A, B, or both

∩

“intersection”

A ∩ B

Only elements in both A and B

-

“set difference”

A-B

Elements in A but not in B

\overline{A} or A^c

“complement”

\overline{A}

Everything not in A

∅

“empty set”

A ∩ B = ∅

No elements in common

¬

not (negation)

∧

“and” (conjunction)

P ∧ Q

Both P and Q must be true

∨

“or” (disjunction)

P∨Q

Either P, or Q, or both

→

implies

P→Q

If P is true, Q must be true

⇔

“if and only if” (iff)

P ⇔ Q

P is true exactly when Q is true

∴

Therefore

P ∴ Q

Used to conclude a result

∀

“for all” (universal quantifier)

∀x ∈ A, P(x)

P is true for every x in A

∃

“there exists”

∃x ∈ A, P(x)

There is at least one x such that P(x) is true

∃!x ∈ A, P(x)

Only one x makes P(x) true

ℕ

Natural numbers

ℕ = {1,2,3,}

Positive integers (sometimes includes 0)

ℤ

Integers

{…, -2, -1, 0, 1, 2, …}

All whole numbers

ℚ

Rational Numbers

1/2 , ¾ ∈ ℚ

Fractions (p/q form)

ℝ

Real numbers, Includes all decimals, π, √2, etc.

C

Complex Numbers

a+bi ∈ C

Numbers with real and imaginary parts