Logic Strand Lecture 3

Example:
Using logically equivalent statements, without the direct
use of truth tables, show: ~ ( ~ p ∧ q) ∧ ( p ∨ q) ≡ p
~
( ~ p ∧ q) ∧ ( p ∨ q) ≡ ( ~ ( ~ p)
∨ ~ q) ∧ ( p ∨ q) ( De Morgan)
≡ ( p ∨ ~ q) ∧ ( p ∨ q) ( Double Negation)
≡ p ∨ ( ~ q ∧ q) ( Distributivity)
≡ p ∨ ( q ∧ ~ q) ( Commutativity)
≡ p ∨ F
( Negation)
≡ p
( Identity)
Exercises:
Using logically equivalent statements, without the direct
use of truth tables, show:
• ~ ( p ⇔ q) ≡ ( p ∧ ~ q) ∨ ( q ∧ ~ p)
WUCT121 Logic 58