Math Symbols and Languages

Question 1

(~) && (¬)

Answer 1

Negations (~x) = (not x)

Question 2

⇔

Answer 2

Equivalent (if and only if) =
p: this year has 366 days
q: this is a leap year
p ⇔ q

Question 3

⇒

Answer 3

Implies (implication) =
p: a number is a multiple of 4
q: the number is even
p ⇒ q

Question 4

∈

Answer 4

Belong to/is an element of (Set membership) =
A = {1, 2, 3}
2 ∈ A

Question 5

∉

Answer 5

Not element of (Negation of set membership) =
A={1, 2, 3}
0 ∉ A

Question 6

∀

Answer 6

for all (Universal Quantifier) =
2n is even ∀ n ∈ N
where N is a set of Natural Numbers

Question 7

∃

Answer 7

there exists (Existential quantifier) =
b is divisible by a, then ∃ n ∈ N such that b = na

Question 8

∄

Answer 8

there does not exist (Negation of existential quantifier) =
b is not divisible by a, then ∄ n ∈ N such that b = na

Question 9

∵

Answer 9

because / since (Because shorthand) =
a = b, b = c
⇒ a = c (∵ a = b)

Question 10

∴

Answer 10

therefore (Therefore shorthand (Logical consequence)) =
x + 6 = 10
∴ x = 4

Question 11

e

Answer 11

e constant / Euler’s number (e = 2.718281828…) =
e = lim (1+1/x)x , x→∞

Question 12

(&), (^) && (·)

Answer 12

Ampersand, Caret & dot (and) =
(a & y), (a ^ y), and (a · y)

Question 13

(|), (∨), (+)

Answer 13

Vertical Line, Reversed Caret, & plus (or) =
(a | y), (a∨y), and (a + y)

Question 14

⊕

Answer 14

circled plus / oplus (exclusive or – xor) = x ⊕ y