LOP Symbols

For making sure I understand the symbols before I get into the names.

¬

not

∧

and

∨

or (at least one true)

⊕

exclusive or (exactly one true)

→

if … then …

↔

if and only if

≡

is logically equivalent to

∀

for all

∃

there exists

∃!

there exists exactly one

⟹

therefore

p → q

if p, then q

¬p

not p

p ∧ q

p and q

p ∨ q

p or q

p ⊕ q

p exclusive or q

p ↔ q

p if and only if q

p ≡ q

p is logically equivalent to q

∀x

for all x

∃x

there exists an x

∃!x

there exists exactly one x

¬q → ¬p

if not q, then not p

¬q, p → q ⟹ ¬p

not q, and if p then q, therefore not p

p, p → q ⟹ q

p, and if p then q, therefore q

,

and / given that

p

a proposition (statement with a truth value)

q

a proposition (statement with a truth value)

r

a proposition (statement with a truth value)