Maharashtra State BoardHSC Arts 12th Board Exam
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Examine whether the following statement pattern is a tautology or a contradiction or a contingency. (p → q) ↔ (∼ p ∨ q) - Mathematics and Statistics

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Sum

Examine whether the following statement pattern is a tautology or a contradiction or a contingency.

(p → q) ↔ (∼ p ∨ q)

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Solution

p q ∼ p p → q ∼ p ∨ q (p → q) ↔ (∼ p ∨ q)
T T F T T T
T F F F F T
F T T T T T
F F T T T T

All the entries in the last column of the above truth table are T.
∴ (p → q) ↔ (∼ p ∨ q) is a tautology.

Concept: Statement Patterns and Logical Equivalence
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