On a multiple-choice test, one of the questions is illegible, but the choice of answers is listed clearly below. What’s the right answer?
(a) All of the below.
(b) None of the below.
(c) All of the above.
(d) One of the above.
(e) None of the above.
(f) None of the above.
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(a) implies that both (b) and (f) are right, which is a contradiction, so (a) can’t be right. And (c) claims that (a) is right, so (c) can’t be right either.
We’ve eliminated (a) and (c). That means that if (b) is a correct statement then (d) is accurate. But (b) contradicts (d), so (b) must be false. And since (a), (b), and (c) are all false, then (d) is false as well.
Now we’re down to (e) and (f). (f) can’t be true, because it implies simultaneously that statements (a) through (d) are false and that (e), which agrees with this, is also false, another contradiction.
That leaves (e), whose truth is confirmed by the falsity of statements (a) through (d).
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