Classical logic

Classic logic is a system for proof

Operators

or                      ∨
and                     ∧
not                     ¬
xor                     ⊕
implies/conditional     →
bimplies/bi conditional ↔
turnstile/proves        ⊢

Truth values

false/absurdum          ⊥      
true/verum              ⊤

Laws

a ⊢ a ∨ b              or intro
a, b ⊢ a ∧ b           and intro
a ∧ b ⊢ a              and elim
a → b ⊢ ¬a ∨ b         implication equiv
¬(a ∨ b) ⊢ ¬a ∧ ¬b    De Morgan's law
¬(a ∧ b) ⊢ ¬a ∨ ¬b    De Morgan's law