The GATE Grind

GATE 2026 MT – Question 4

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

‘All the mangoes in the basket are good.’ If the above statement is false, then which one of the following statements is necessarily true?

  1. All the mangoes in the basket are not good.
  2. No mango in the basket is good.
  3. In the basket, some of the mangoes are good and some are not good.
  4. There exists at least one mango in the basket that is not good.

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Show answer and explanation

Correct answer: (D) There exists at least one mango in the basket that is not good.

Explanation

The negation of a universal statement is the existence of a counterexample: not every mango is good means at least one mango is not good. It does not require all mangoes to be bad or require a mixture of good and bad. Thus **D** is necessarily true.