Discussion
'All the mangoes in the basket are good.'
If the above statement is false, then which one of the following statements is necessarily true?
Answer: D
The statement that must be true is There exists at least one mango in the basket that is not good.
'All the mangoes are good' is false exactly when at least one mango is not good; that is its logical negation, so it is necessarily true.
The other options say more than the negation allows. 'All the mangoes are not good' and 'No mango is good' claim every mango is bad, but the statement is also false when just one mango is bad. 'Some are good and some are not' requires at least one good mango, which is not guaranteed: every mango could be bad.
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