"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
- 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.
The Correct Option is D
Solution and Explanation
The original claim is a universal statement: every mango in the basket is good. Denying a universal statement does not flip it into another universal statement; it only needs one exception to exist.
- All the mangoes are not good: this reads as a second universal claim that every mango is bad, which is stronger than what a false original statement requires.
- No mango is good: this again claims every single mango is bad, which is more than the negation demands.
- Some are good and some are not good: this is one possible situation, but a false original statement does not force this exact split; there could be zero good mangoes too.
- At least one mango is not good: this is the precise logical negation of "all mangoes are good," and it holds in every case where the original statement fails.
Since only the fourth option must be true whenever the original statement is false, it is the correct choice.
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