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

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Using the truth table prove the following logical equivalence.

p ↔ q ≡ ∼ [(p ∨ q) ∧ ∼ (p ∧ q)]

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Solution

1 2 3 4 5 6 7 8
p q p ↔ q p ∨ q p ∧ q ∼ (p ∧ q) (p ∨ q) ∧ ∼ (p ∧ q) ∼ [(p ∨ q) ∧ ∼ (p ∧ q)]
T T T T T F F T
T F F T F T T F
F T F T F T T F
F F T F F T F T

The entries in columns 3 and 8 are identical.
∴ p ↔ q ≡ ∼ [(p ∨ q) ∧ ∼ (p ∧ q)]

Concept: Statement Patterns and Logical Equivalence
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