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

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Using the truth table proves the following logical equivalence.

∼ (p ↔ q) ≡ (p ∧ ∼ q) ∨ (q ∧ ∼ p)

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Solution

1 2 3 4 5 6 7 8 9
p q ∼ p ∼ q p ↔ q ∼ (p ↔ q) p ∧ ∼ q q ∧ ∼ p (p ∧ ∼ q) ∨ (q ∧ ∼ p)
T T F F T F F F F
T F F T F T T F T
F T T F F T F T T
F F T T T F F F F

The entries in columns 6 and 9 are identical.
∴ ∼ (p ↔ q) ≡ (p ∧ ∼ q) ∨ (q ∧ ∼ p)

Concept: Statement Patterns and Logical Equivalence
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