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GATE 2016 ME (ME2) – Question 4

General Aptitude · Analytical Aptitude: Logical Reasoning and Deduction · 1 mark · Multiple choice

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?

  1. If (iii), then (iv).
  2. If (i), then (iii).
  3. If (i), then (ii).
  4. If (ii), then (iv).

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Show answer and explanation

Correct answer: (C) If (i), then (ii).

Explanation

The premise is R implies W. A situation with R true and W false directly violates this implication, so rain together with a field that is not wet is impossible under the fact. This is **C**. Not wet implies no rain is the valid contrapositive.