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Determine whether the following statement pattern is a tautology, contradiction, or contingency. [P → (~q ∨ r)] ↔ ~[p → (q → r)] - Mathematics and Statistics

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Question

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

[p → (~q ∨ r)] ↔ ~[p → (q → r)]

Sum
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Solution

p q r ~q ~q∨r q→r p→(q→r) p→(~q∨r) ~[p→(q→r)] [p→(~q∨r)]↔~[p → (q → r)]
T T T F T T T T F F
T T F F F F F F T F
T F T T T T T T F F
T F F T T T T T F F
F T T F T T T T F F
F T F F F F T T F F
F F T T T T T T F F
F F F T T T T T F F

All the truth values in the last column are F. Hence, it is contradiction.

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Chapter 1: Mathematical Logic - Miscellaneous Exercise 1 [Page 33]

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Balbharati Mathematics and Statistics 1 (Commerce) [English] Standard 12 Maharashtra State Board
Chapter 1 Mathematical Logic
Miscellaneous Exercise 1 | Q 4.13 | Page 33
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