📐 Propositional calculus formulas

Proven via truth table

Name	Formula	Equivalent
De Morgan I	p∨q	¬(¬p ∧ ¬q)
De Morgan II	p∧q	¬(¬p ∨ ¬q)
Distributive law I	p ∧ (q ∨ r)	(p ∧ q) ∨ (p ∧ r)
Distributive law II	p ∨ (q ∧ r)	(p ∨ q) ∧ (p ∨ r)
Reduction of the conditional I	p→q	¬p ∨ q
Reduction of the conditional II	p→q	¬(p ∧ ¬q)
Contraposition of the conditional	p→q	¬q → ¬p
Im/Export	(p ∧ q) → r	p → (q → r)
Reduction of the biconditional	p↔q	(p → q) ∧ (q → p)
Contraposition of the biconditional	p↔q	¬q ↔ ¬p
Reduction of the exclusive disjunction	p≻≺q	¬(¬A∨B)∨¬(A∨¬B)