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JEE Main 201323 AprilOnline

Exam: JEE Main
Year: 2013
Date: 23 April
Mode: Online
Subject: Mathematics
Chapter: Mathematical Reasoning

JEE Main 2013 · 23 April · Online · Mathematics · Mathematical Reasoning

For integers m and n , both greater than 1, consider the following...

For integers

m

and

n

, both greater than 1, consider the following three statements :

P: m

divides

n

Q: m

divides

n^2

R: m

is prime, then

Options

A $Q \wedge R \rightarrow P$
B $P \wedge Q \rightarrow R$
C $Q \rightarrow R$
D $Q \rightarrow P$

Correct answer

A. $Q \wedge R \rightarrow P$

Step-by-step solution

(b)

\frac{8}{4}=2, \frac{64}{4}=16

; but 4 is not prime. Hence

\mathrm{P} \wedge \mathrm{Q} \rightarrow \mathrm{R}

, false (c)

\frac{(6)^2}{12}=\frac{36}{12}=3

; but 12 is not prime Hence

Q \rightarrow R

, false (d)

\frac{(4)^2}{8}=\frac{16}{8}=2 ; \frac{4}{8}

is not an integer Hence

\mathrm{Q} \rightarrow \mathrm{P}

, false

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