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Using the truth table, verify p ∨ (q ∧ r) ≡ (p ∨ q) ∧ (p ∨ r) - Mathematics and Statistics

Sum

Using the truth table, verify

p ∨ (q ∧ r) ≡ (p ∨ q) ∧ (p ∨ r)

Prove that the following pair of statement patterns is equivalent.

p ∨ (q ∧ r) and (p ∨ q) ∧ (p ∨ r)

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Solution

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 columns 5 and 8 are identical.

∴ p ∨ (q ∧ r) ≡ (p ∨ q) ∧ (p ∨ r)

  Is there an error in this question or solution?
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