Question

Consider the following three statements:
(A) If $3 + 2 = 7$ then $4 + 3 = 8$.
(B) If $5 + 2 = 7$ then earth is flat.
(C) If both (A) and (B) are true then $5 + 6 = 11$.
Which of the following statements is correct?

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

Hint:

In formal logic, a conditional statement is vacuously true whenever the "If" part (the premise) is false. If you start with a lie, you can logically conclude absolutely anything! (False $\rightarrow$ True = True, and False $\rightarrow$ False = True).

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
In mathematical logic, a conditional statement $p \rightarrow q$ is false only when the antecedent ($p$) is true and the consequent ($q$) is false. In all other cases, it is true.

Step 2: Formula Application:
(A) $3+2=7$ (False) $\rightarrow 4+3=8$ (False). $F \rightarrow F$ is True. (B) $5+2=7$ (True) $\rightarrow$ Earth is flat (False). $T \rightarrow F$ is False.

Step 3: Explanation:
(C) "If both (A) and (B) are true" $\rightarrow 5+6=11$. Since (B) is false, the compound antecedent "(A) and (B)" is False. (False) $\rightarrow (5+6=11)$ (True). $F \rightarrow T$ is True.

Step 4: Final Answer:
Statement (A) is true, (B) is false, and (C) is true.