Exams › GATE › General Aptitude

Consider the following three statements: (i) Some roses are red. (ii) All red flowers fade quickly. (iii) Some roses fade quickly. Which of the following statements can be logically inferred from the above statements?

1. If (i) is true and (ii) is false, then (iii) is false.
2. If (i) is true and (ii) is false, then (iii) is true.
3. If (i) and (ii) are true, then (iii) is true.
4. If (i) and (ii) are false, then (iii) is false.

Correct answer: If (i) is true and (ii) is false, then (iii) is false.

Solution

Statement (iii) follows only if some roses are red and all red flowers fade quickly. If (ii) is false, then being red does not guarantee fading quickly, so (iii) cannot be logically concluded from (i) alone. Hence the only valid inference among the options is that (iii) is false when (i) is true and (ii) is false.

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