# Question: use the laws of propositional logic to prove the following...

###### Question details

Use the laws of propositional logic to prove the following:

A) (p ∧ q ∧ ¬r) ∨ (p ∧ ¬q ∧ ¬r) ≡ p ∧ ¬r

B) p ↔ (p ∧ r) ≡ ¬p ∨ r

C) (p ∧ q) → r ≡ (p ∧ ¬r) → ¬q

Use the laws of propositional logic to prove the following:

A) (p ∧ q ∧ ¬r) ∨ (p ∧ ¬q ∧ ¬r) ≡ p ∧ ¬r

B) p ↔ (p ∧ r) ≡ ¬p ∨ r

C) (p ∧ q) → r ≡ (p ∧ ¬r) → ¬q