Maharashtra State BoardHSC Arts 12th Board Exam
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Using the truth table prove the following logical equivalence. p ∧ (q ∨ r) ≡ (p ∧ q) ∨ (p ∧ r) - Mathematics and Statistics

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Using the truth table prove the following logical equivalence.

p ∧ (q ∨ r) ≡ (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 T T T F T
T F T T T F T T
T F F F F F F F
F T T T F F F F
F T F T F F F F
F F T T F F F 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)

Concept: Statement Patterns and Logical Equivalence
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