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JEE Main 20169 AprilOnline
Exam
JEE Main
Year
2016
Date
9 April
Mode
Online
Subject
Mathematics
Chapter
Mathematical Reasoning

JEE Main 2016 · 9 April · Online · Mathematics · Mathematical Reasoning

Consider the following two statements: P : If 7 is an odd number,...

Consider the following two statements:

PP : If 77 is an odd number, then 77 is divisible by 22.

QQ : If 77 is a prime number, then 77 is an odd number.

If V1{V}_{1} is the truth value of the contrapositive of PandV2P and {V}_{2} is the truth value of contrapositive of QQ, then the ordered pair (V1,V2)\left({V}_{1}, {V}_{2}\right) equals

Options

  1. A(F,T)\left(F, T\right)
  2. B(F,F)\left(F, F\right)
  3. C(T,F)\left(T, F\right)
  4. D(T,T)\left(T, T\right)

Correct answer

A. (F,T)\left(F, T\right)

Step-by-step solution

Contrapositive of P:P:

77 is not divisible by 2⇒72 ⇒ 7 is not odd number

T⇒F:F(V1)<br/><br/>ContrapositiveT ⇒ F: F \left({V}_{1}\right)<br /><br />Contrapositive of Q:<br/><br/><br /><br />7isnotoddnumberis not odd number⇒ 7isnotaprimenumber<br/><br/>is not a prime number <br /><br />F ⇒ F: T \left({V}_{2}\right)</p><p>Thus,(V1,V2)≡(F,T)</p></p><p>Thus, \left({V}_{1}, {V}_{2}\right) ≡ \left(F, T\right)</p>

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