Consider the following three statements :
(A) if then .
(B) If then earth is flat.
(C) If both (A) and (B) are true then .
Then, which of the following statements is correct?
(A) if then .
(B) If then earth is flat.
(C) If both (A) and (B) are true then .
Then, which of the following statements is correct?
- (A)(A) and (C) are true while (B) is false✓ Correct
- (B)(A) and (B) are false while (C) is true
- (C)(A) is true while (B) and (C) are false
- (D)(A) is false, but (B) and (C) are true
Answer: (A)
Solution
An implication is false only when its hypothesis is true and its conclusion false; a false hypothesis makes the whole implication true. In the first statement the hypothesis is false, so the first statement is true. In the second statement the hypothesis is true while the conclusion that the earth is flat is false, so the second statement is false. The third statement has as its hypothesis that the first two statements are both true, and that hypothesis is false because the second statement is false, so the third statement is true. Hence the first and third statements are true while the second statement is false.
JEE Main · 2021 · 20 Jul 2021 · Shift 2 · Single correct option