Question
Using the truth table, prove the following logical equivalences:
p ↔ q ≡ ~(p ∧ ~q) ∧ ~(q ∧ ~p)
p ↔ q ≡ ~(p ∧ ~q) ∧ ~(q ∧ ~p)
✓
Answer
p ↔ q ≡ ~(p ∧ ~q) ∧ ~(q ∧ ~p)
The entries in columns 3 and 10 are identical.
∴ p ↔ q ≡ ~(p ∧ ~q) ∧ ~(q ∧ ~p)
The entries in columns 3 and 10 are identical.
∴ p ↔ q ≡ ~(p ∧ ~q) ∧ ~(q ∧ ~p)
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