Consider :
Statement - I : \((p\wedge\sim q)\wedge(\sim p\wedge q)\) is a fallacy.
Statement - II : \((p\to q)\leftrightarrow(\sim q\to\sim p)\) is a tautology.
Statement - I : \((p\wedge\sim q)\wedge(\sim p\wedge q)\) is a fallacy.
Statement - II : \((p\to q)\leftrightarrow(\sim q\to\sim p)\) is a tautology.
Show Hint
- Statement - I is True; Statement -II is true; Statement-II is not a correct explanation for Statement-I
- Statement -I is True; Statement -II is False.
- Statement -I is False; Statement -II is True
- Statement -I is True; Statement -II is True; Statement-II is a correct explanation for Statement-I
The Correct Option is A
Solution and Explanation
Statement-II: \(\sim q\to\sim p\) is the contrapositive of \(p\to q\), so they are logically equivalent. Hence \((p\to q)\leftrightarrow(\sim q\to\sim p)\) is always true, a tautology. Statement-II is true.
Statement-II is about contrapositive equivalence and has no bearing on why the statement in I is a contradiction, so it is not an explanation of Statement-I.
Answer: (1) Statement - I is True; Statement -II is true; Statement-II is not a correct explanation for Statement-I
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