Which set contains exactly one true statement?

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Multiple Choice

Which set contains exactly one true statement?

Explanation:
This question hinges on how self-referential statements about the total number of true statements behave. Each Fi is tied to a claim about how many of the ten statements are true, so to have exactly one true statement in a chosen group, that group must be able to satisfy the count with a single truthful statement while all others in the group stay false. The set containing F1, F3, F5, and F9 is the one that can fit that requirement: it permits exactly one of its members to be true without forcing another within the same group to also be true, and it avoids contradictions that would arise if more than one or none were true. In contrast, any other grouping would, under the same rules, push the count toward multiple truths or zero truths, which violates the condition of "exactly one true statement." So, this set is the only arrangement among the options that can consistently yield exactly one true statement.

This question hinges on how self-referential statements about the total number of true statements behave. Each Fi is tied to a claim about how many of the ten statements are true, so to have exactly one true statement in a chosen group, that group must be able to satisfy the count with a single truthful statement while all others in the group stay false.

The set containing F1, F3, F5, and F9 is the one that can fit that requirement: it permits exactly one of its members to be true without forcing another within the same group to also be true, and it avoids contradictions that would arise if more than one or none were true. In contrast, any other grouping would, under the same rules, push the count toward multiple truths or zero truths, which violates the condition of "exactly one true statement."

So, this set is the only arrangement among the options that can consistently yield exactly one true statement.

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