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If p and q are two statements then (p → q) ↔ (∼ q → ∼ p) is ______. - Mathematics and Statistics

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Question

If p and q are two statements then (p → q) ↔ (∼ q → ∼ p) is ______.

Options

  • Contradiction

  • Tautology

  • Neither (i) not (ii)

  • None of the these

MCQ
Fill in the Blanks
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Solution

If p and q are two statements then (p → q) ↔ (∼ q → ∼ p) is Tautology.

Explanation:

pq ~q → ~p q → p ↔ ~q ↔ ~p
T T T
F F T
T T T
T T T

Therefore, it is a tauology 

Hence, the given proposition is a tautology.

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Chapter 1: Mathematical Logic - Miscellaneous Exercise 1 [Page 30]

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