Question
Using truth table prove that p ˅ (q ˄ r) ≡ (p ˅ q) ˄ (p ˅ r).

Answer

p ∨ (q ∧ r) ≡ (p ∨ q) ∧ (p ∨ r)

1 2 3 4 5 6 7 8
p q r q ∧ r p ∨ (q ∧ r) p ∨ q p ∨ r (p ∨ q) ∧ (p ∨ r)
T T T T T T T T
T T F F T T T T
T F T F T T T T
T F F F T T T T
F T T T T T T T
F T F F F T F F
F F T F F F T F
F F F F F F F F

The entries in the columns 5 and 8 are identical.

∴ p ∨ (q ∧ r) ≡ (p ∨ q) ∧ (p ∨ r)

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