JEE Main 2013MathematicsMathematical ReasoningMediumMCQ

JEE Main 2013 — Mathematical Reasoning Question with Solution

JEE Main 2013 (07 Apr)

Question

Consider :
Statement - I : p∧~q∧~p∧q is a fallacy.
Statement - II : p→q↔~q→~p is a tautology.

Choose an option

Show full solutionCorrect option: D
Correct answer
DStatement - I is true; Statement - II is true; Statement - II is not a correct explanation for Statement - I.

Step-by-step explanation

The truth table for Statement I is

p q ~p ~q p∧~q ~p∧q p∧~q∧~p∧q

TTFF

 TFTF FFTT FTFT FTFF FFTF

FFFF

Hence, it is a fallacy. 

The truth table for statement II is

p q ~p ~q p→q ~q→~p p→q↔~q→~p
TTFF TFTF FFTT FTFT TFTT TFTT TTTT

Hence, it is a tautology.

But, the second statement is not a correct explanation for the first.

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About this question

This is a previous-year question from JEE Main 2013, covering the Mathematical Reasoning chapter of Mathematics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.