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 - Mathematics and Statistics

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Using the truth table prove the following logical equivalence.

∼ (p ∨ q) ∨ (∼ p ∧ q) ≡ ∼ p

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Solution

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

The entries in columns 3 and 7 are identical.
∴ ∼ (p ∨ q) ∨ (∼ p ∧ q) ≡ ∼ p

Concept: Statement Patterns and Logical Equivalence
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