The Six Sentences

Logic Level 2

Exactly one of these sentences is true.

(1): Statement 2 is true.
(2): Statement 1 is false.
(3): None of these statements are true.
(4): Statement 3 is true.
(5): Statement 4 is true.
(6): Statement 2 is false.
(7): Statement 3 is true.

Which of these statements must be true?

6 1 7 5 4 This is an impossible situation 2 3

2 solutions

Siva Budaraju
Feb 28, 2017

All you have to do is look at the first two statements. If one is true, two is true, but then one is false, which is a contradiction. So one must be false. But if one is false, two is false, which means one is true, which is also a contradiction! So just by looking at statements one and two, we have already proved that the whole scenario is impossible.

Kriya Jaiganesh
Feb 20, 2017

If one is true, then 2 is true(read number two) If two is true, then one is false(read number one) If three is true, then none are true, but look again. The answer may seem like this one, but it's a trick. If none are true, then how come number three is? If four is true, then three is true(read number three) If five is true, then 4 is true(read number four) If six is true, then one is true(read number one) If seven is true, then three is true(read number three)

I didn't explain it, but if one were to be true, the whole problem would become seriously complicated and confusing!

You could have just focused on statements 1 and 2 to explain why it's an impossible scenario. It's then independent of what the other statements say, the system will be inconsistent.

Calvin Lin Staff - 4 years, 3 months ago

The Six Sentences

2 solutions

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