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

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Sum

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

[~(p ∧ q) → p] ↔ [(~p) ∧ (~q)]

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Solution

p q ~p ~q p∧q ~(p∧q) ~(p∧q)→p (~p)∧(~q) [~(p∧q)→p]↔[(~p)∧(~q)]
T T F F T F T F F
T F F T F T T F F
F T T F F T F F T
F F T T F T F T F

Truth values in the last column are not identical. Hence, it is contingency.

Concept: Statement Patterns and Logical Equivalence
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APPEARS IN

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