MHTCET 22 Apr 2025 Shift 2 Paper

Concept:A conditional statement and its contrapositive are logically equivalent.So we find the truth value of each contrapositive by checking its antecedent and consequent directly.Explanation:For $p$: "If 7 is an odd number then 7 is divisible by 2."Here, "7 is an odd number" is true, and "7 is divisible by 2" is false.So $p$ is $\mathrm{T} \to \mathrm{F} \equiv \mathrm{F}$.The contrapositive of $p$ is: "If 7 is not divisible by 2 then 7 is not an odd number.""7 is not divisible by 2" is true, and "7 is not an odd number" is false.Therefore, $V_1 \equiv \mathrm{T} \to \mathrm{F} \equiv \mathrm{F}$.For $q$: "If 7 is prime number then 7 is an odd number."Here, "7 is prime number" is true, and "7 is an odd number" is true.So $q$ is $\mathrm{T} \to \mathrm{T} \equiv \mathrm{T}$.The contrapositive of $q$ is: "If 7 is not an odd number then 7 is not prime number.""7 is not an odd number" is false, and "7 is not prime number" is false.Therefore, $V_2 \equiv \mathrm{F} \to \mathrm{F} \equiv \mathrm{T}$.Answer:$\left(V_1, V_2\right) \equiv (\mathrm{F}, \mathrm{T})$, i.e. option C.