Consider : Statement - I: \((p \wedge \sim q) \wedge(\sim p \wedge q)\) is a fallacy. Statement - II : \((p \rightarrow q) \leftrightarrow(\sim q \rightarrow \sim p)\) is a tautology.

(A) Statement - I is True; Statement -II is true; Statement-II is not a correct explanation for Statement-I

(B) Statement -I is True; Statement -II is False.

(C) Statement -I is False; Statement -II is True

(D) Statement -I is True; Statement -II is True; Statement-II is a correct explanation for Statement-I

Mathematical Reasoning * — JEE Main · 2013 · 07 Apr 2013 · Offline Question with Solution

Consider :

Statement - I:

(p \land \sim q) \land (\sim p \land q)

is a fallacy.

Statement - II :

(p \to q) \leftrightarrow (\sim q \to\sim p)

is a tautology.

(A)Statement - I is True; Statement -II is true; Statement-II is not a correct explanation for Statement-I✓ Correct
(B)Statement -I is True; Statement -II is False.
(C)Statement -I is False; Statement -II is True
(D)Statement -I is True; Statement -II is True; Statement-II is a correct explanation for Statement-I

Answer: (A)

Solution

Statement I pairs

p \land \sim q

with

\sim p \land q

; since this demands both

p

and

\sim p

at once, it can never be true and is indeed a fallacy. Statement II asserts that an implication equals its contrapositive,

(p \to q) \leftrightarrow (\sim q \to\sim p)

, which is a genuine tautology. Both statements are true, but the contrapositive equivalence has nothing to do with why the first expression is always false, so the second is not an explanation of the first.

JEE Main · 2013 · 07 Apr 2013 · Offline · Single correct option

JEE Main · 2013 · 07 Apr 2013 · Offline · Mathematical Reasoning *

Solution

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