QJEEM13Ma9836: JEE Main 2013 Mathematics - Class 11 JEEM13Ma9836 Solution: Consider : Statement − I : is a fallacy. Statement − II : is a…

Question

Verified Solution • 2025–26 Session moderate

Consider :
Statement − I :

\left( {p \wedge \sim q} \right) \wedge \left( { \sim p \wedge q} \right)

is a fallacy.
Statement − II :

\left( {p \to q} \right) \leftrightarrow \left( { \sim q \to \sim p} \right)

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

Accepted Answer

Statement - I : $(p \wedge \sim q) \wedge ( \sim p \wedge q)$

p	q	$\sim p$	$\sim q$	$p \wedge \sim q$	$\sim p \wedge q$	$(p \wedge \sim q) \wedge ( \sim p \wedge q)$
T	T	F	F	F	F	F
T	F	F	T	T	F	F
F	T	T	F	F	T	F
F	F	T	T	F	F	F

Hence, statement-I is a fallacy.

Statement - II : $(p \to q) \leftrightarrow ( \sim q \to \sim p)$

p	q	$\sim p$	$\sim q$	$p \to q$	$\sim q \to \sim p$	$(p \to q) \leftrightarrow ( \sim q \to \sim p)$
T	T	F	F	T	T	T
T	F	F	T	F	F	T
F	T	T	F	T	T	T
F	F	T	T	T	T	T

Hence, statement - II is a tautology.

Now, statement-II does not depend on statement-I.

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