Question:easy

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

Show Hint

Negating "all X are good" gives "at least one X is not good".
Updated On: Jul 27, 2026
  • All the mangoes in the basket are not good.
  • No mango in the basket is good.
  • In the basket, some of the mangoes are good and some are not good.
  • There exists at least one mango in the basket that is not good.
Show Solution

The Correct Option is D

Solution and Explanation

Step 1: Write the statement in logical form.
Let $G(m)$ mean "mango $m$ is good". The claim "all the mangoes are good" is $\forall m, G(m)$.
Its negation is $\exists m, \neg G(m)$, meaning at least one mango fails to be good.

Step 2: Match this to the given options.
"All are not good" and "no mango is good" both mean $\forall m, \neg G(m)$, a stronger claim than the negation, so they are not forced to be true.
"Some good and some not good" is only one specific case among many that satisfy $\exists m, \neg G(m)$, so it need not always hold.

Final Answer:
Only "there exists at least one mango that is not good" matches $\exists m, \neg G(m)$ exactly.\[ \boxed{\text{At least one mango in the basket is not good}} \]
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