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 F T F
T F T T F F
F T F F T F
F F T F T F

All the entries in the last column of the above truth table are F.
∴ (p ∧ ∼ q) ↔ (p → q) is a contradiction.
[Note: Answer in the textbook is incorrect]

Concept: Statement Patterns and Logical Equivalence
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