- Home
- Standard 11
- Mathematics
Mathematical Reasoning
hard
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 true statement is
A
$Q \wedge R \to P$
B
$P \wedge Q \to R$
C
$Q \to R$
D
$Q \to P$
(JEE MAIN-2013)
Solution
$\left( b \right)\,\,\,\,\,\,\,\frac{8}{4} = 2,\frac{{64}}{4} = 16;$ but $4$ is not prime.
Hence ${P \wedge Q \to R}$, false
$\left( c \right)\,\,\,\,\,\,\,\frac{{{{\left( 6 \right)}^2}}}{{12}} = \frac{{36}}{{12}} = 3;$ but $12$ is not prime
Hence ${Q \to R}$, false
$\left( d \right)\,\,\,\,\,\,\,\frac{{{{\left( 4 \right)}^2}}}{8} = \frac{{16}}{8} = 2;\frac{4}{8}$ is not an Integer
Hence ${Q \to P}$, flase
Standard 11
Mathematics
