Q55 / 150 · MHT CET 2025 (25 Apr Shift 2) · Mathematics
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?
- Correct answerA(A) and (C) are true while (B) is false.
- B(A) is true while (B) and (C) are false.
- C(A) is false but (B) and (C) are true.
- D(A) is false while (C) is true.
Solution
A conditional statement $P \implies Q$ is false only when $P$ is true and $Q$ is false. In all other cases, it is true.
Statement A: If $3+2=7$ then $4+3=8$.
The antecedent $3+2=7$ is false, and the consequent $4+3=8$ is also false. Since the antecedent is false, the entire implication is true.
Statement B: If $5+2=7$ then Earth is flat.
The antecedent $5+2=7$ is true, but the consequent "Earth is flat" is false. With a true antecedent and false consequent, the implication is false.
Statement C: If both A and B are true then $5+6=11$.
The antecedent "both A and B are true" is false because B is false, and the consequent $5+6=11$ is true. Since the antecedent is false, the implication is true.
Therefore, A and C are true while B is false, which corresponds to option A.
Hence, the correct answer is option: 'A'.