Question

Consider the statements given by following
(A) If 4+3 = 8, then 5+3=9
(B) If 6 + 4 = 10, then moon is flat
(C) If both (A) and (B) are true, then 5 + 6 = 17
Then which of the following statement is correct?

• (A) is true while (B) and (C) are false
• (A) and (B) are false, while (C) is true
• (A) and (C) are true, while (B) is false
• (A) is false, but (B) and (C) are true

Hint:

A conditional statement $p \to q$ is only false when $p$ is True and $q$ is False.

Answer 1

The Correct Option is C

Step 1: Evaluate (A)
$p \to q$ where $p = (4+3=8)$ is False.
$F \to (\text{anything})$ is always True. So (A) is True.
Step 2: Evaluate (B)
$p \to q$ where $p = (6+4=10)$ is True, and $q = (\text{moon is flat})$ is False.
$T \to F$ is False. So (B) is False.
Step 3: Evaluate (C)
"If (A) and (B) are true" $\implies (T \land F) = False$.
Again, $F \to (\text{anything})$ is True. So (C) is True.
Step 4: Conclusion
(A) and (C) are true, (B) is false.
Final Answer:(C)