Using the laws of logic to prove logical equivalence.

Use the laws of propositional logic to prove the following:

(p ∧ q) → r ≡ (p ∧ ¬r) → ¬q

Idempotent laws:	p ∨ p ≡ p	p ∧ p ≡ p
Associative laws:	( p ∨ q ) ∨ r ≡ p ∨ ( q ∨ r )	( p ∧ q ) ∧ r ≡ p ∧ ( q ∧ r )
Commutative laws:	p ∨ q ≡ q ∨ p	p ∧ q ≡ q ∧ p
Distributive laws:	p ∨ ( q ∧ r ) ≡ ( p ∨ q ) ∧ ( p ∨ r )	p ∧ ( q ∨ r ) ≡ ( p ∧ q ) ∨ ( p ∧ r )
Identity laws:	p ∨ F ≡ p	p ∧ T ≡ p
Domination laws:	p ∧ F ≡ F	p ∨ T ≡ T
Double negation law:	¬¬p ≡ p
Complement laws:	p ∧ ¬p ≡ F ¬T ≡ F	p ∨ ¬p ≡ T ¬F ≡ T
De Morgan's laws:	¬( p ∨ q ) ≡ ¬p ∧ ¬q	¬( p ∧ q ) ≡ ¬p ∨ ¬q
Absorption laws:	p ∨ (p ∧ q) ≡ p	p ∧ (p ∨ q) ≡ p
Conditional identities:	p → q ≡ ¬p ∨ q	p ↔ q ≡ ( p → q ) ∧ ( q → p )

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