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 F F T F F
T F T F F F T F
T F F F F F F F
F T T T T T T T
F T F F T T T T
F F T F T T T T
F F F F T T T T

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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