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

The entries in the last column of the above truth table are neither all T nor all F.
∴ (p ↔ q) ∧ (p → ∼ q) is a contingency.

Concept: Statement Patterns and Logical Equivalence
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