Question

$p$ : If 7 is an odd number then 7 is divisible by 2.
$q$ : If 7 is prime number then 7 is an odd number. If $V_1$ and $V_2$ are respective truth values of contrapositive of p and q then $(V_1, V_2) \equiv$

• A. (T, T)
• B. (T, F)
• C. (F, T)
• D. (F, F)

Hint:

Contrapositive $\equiv$ Original Statement. No need to rewrite the sentence.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
A statement and its contrapositive always have the same truth value.
So we can just find the truth values of the original statements $p$ and $q$.
Step 2: Key Formula or Approach:
Truth table for $P \rightarrow Q$ is False ONLY when $P$ is True and $Q$ is False.
Contrapositive of $P \rightarrow Q$ is $\neg Q \rightarrow \neg P$.
Step 3: Detailed Explanation:
Statement $p$: "7 is odd" (T) $\rightarrow$ "7 is divisible by 2" (F).
Truth value of $p$ is $T \rightarrow F$, which is F. Thus $V_1 = F$.

Statement $q$: "7 is prime" (T) $\rightarrow$ "7 is odd" (T).
Truth value of $q$ is $T \rightarrow T$, which is T. Thus $V_2 = T$.
Step 4: Final Answer:
$(V_1, V_2) \equiv (F, T)$.