Four cards lie on a table. Each card has a number printed on one side and a colour on the other. The faces visible on the cards are 2, 3, red, and blue. Proposition: If a card has an even value on one side, then its opposite face is red. The card(s) which MUST be turned over to verify the above proposition are A. 2, red B. 2, 3, red C. 2, blue D. 2, red, blue

GATE 2017 · General Aptitude · Logical Reasoning · medium

Answer: C. 2, blue

1. Identify which visible faces could be counterexamples: P = 'even number', Q = 'back is red'. Counterexample: even number AND back is NOT red.
2. Card '2': must flip: Card shows 2 (even). If back is blue or any non-red, the rule is violated. Must flip to verify back is red.
3. Card '3': skip: Card shows 3 (odd). P is false regardless of back colour. Rule cannot be violated. No need to flip.
4. Card 'red': skip: Card shows red. Q is already true (back is red). Rule cannot be violated regardless of the number on back.
5. Card 'blue': must flip: Card shows blue (not red). By contrapositive: if back is red is false, then front must not be even. Must flip to check that back is not an even number.
6. Conclude: flip 2 and blue: Cards to flip: 2 (check it has red back) and blue (check it does not have an even number on back). Answer: C.