GATE ME 2026 Set 1 — Question 4
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General Aptitude → Analytical Aptitude → Deduction & Induction
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Question
‘All the mangoes in the basket are good.’If the above statement is false, then which one of the following statements is necessarily true?
Correct answer
(D) There exists at least one mango in the basket that is not good.
Solution
The statement “All the mangoes in the basket are good” is a universal statement, . If it is false, its negation must be true. The negation of “all are good” is : there is at least one mango in the basket that is not good.
- (A) “All the mangoes are not good” (none good) is stronger than the negation; it need not hold.
- (B) “No mango is good” is the same as (A); not necessary.
- (C) requires some mangoes to be good as well; if every mango is bad, (C) fails, so it is not necessary.
- (D) is exactly the negation, so it is necessarily true.
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