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Mathematical Reasoning
hard
Consider the following two statements :
$P :$ lf $7$ is an odd number, then $7$ is divisible by $2.$
$Q :$ If $7$ is a prime number, then $7$ is an odd number.
lf $V_1$ is the truth value of the contrapositive of $P$ and $V_2$ is the truth value of contrapositive of $Q,$ then the ordered pair $(V_1, V_2)$ equals
A
$(F, F)$
B
$(F, T)$
C
$(T, F)$
D
$(T, T)$
(JEE MAIN-2016)
Solution
Contra positive of $P:$
$T$ is not divisible by $2 \Rightarrow T$ is not odd number
$T \Rightarrow F:F\left( {{V_1}} \right)$
Contra positive $Q:$
$T$ is not odd number $ \Rightarrow $ $T$ is not a prime number
$F \Rightarrow F:T\left( {{V_2}} \right)$
Standard 11
Mathematics
