Fact: If it rains, then the field is wet. Read the following statements: i. It rains ii. The field is not wet iii. The field is wet iv. It did not rain Which one of the options given below is NOT logically possible, based on the given fact? A. If (i), then (iv). B. If (i), then (iii). C. If (i), then (ii). D. If (ii), then (iv).

GATE 2016 · General Aptitude · Statements Follow · medium

Answer: Option C (If it rains, then the field is NOT wet) directly contradicts the base fact and is NOT logically possible. Answer: C.

1. State the base fact in formal logic: Base fact: rain -> wet_field. The only forbidden row is: rain = TRUE and wet_field = FALSE.
2. Check Option A: If (i) then (iv) — rain -> NOT rain: This conditional means: whenever it rains, conclude it did not rain. This forces the antecedent (rain) to always be false — meaning it simply never rains. That is logically consistent with the base fact (no rain means we never trigger rain -> wet). Option A is possible.
3. Check Option B: If (i) then (iii) — rain -> field is wet: This is exactly the base fact itself: rain -> wet. This is directly supported. Option B is logically possible (and is the direct restatement of the fact).
4. Check Option C: If (i) then (ii) — rain -> field is NOT wet: This says: rain -> NOT wet. But the base fact says: rain -> wet. If it rains, the field must be wet (base fact) AND must not be wet (option C). This is a direct contradiction. Option C is NOT logically possible.
5. Check Option D: If (ii) then (iv) — NOT wet -> NOT rain: The contrapositive of the base fact (rain -> wet) is: NOT wet -> NOT rain. Option D is the contrapositive of the base fact, which is always logically equivalent and thus always valid. Option D is logically necessary.