Question

Consider the following two statements:
P: If $7$ is an odd number, then $7$ is divisible by $2$.
Q: If $7$ is a prime number, then $7$ is an odd number.
If $V_1$ 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. $(T,T)$
• C. $(T,F)$
• D. $(F,T)$

Answer 1

The correct option is D $(F,T)$

The truth value of statement $P$ is $F$ as a True statement cannot

imply a false statement.

The truth value of statement $Q$ is $T$ as True statement implying True statement is $T$

The truth value of a conditional and its contra-positive are logically equivalent.

Hence $V_1$ is $F$ and $V_2$ is $T$