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. ∼ (∼ 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.

∼ (∼ q ∧ p) ∧ q

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Solution

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

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

Concept: Statement Patterns and Logical Equivalence
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