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Each of the following five statements is either true or false.

A. Statement D is true, or statement E is false, or the moon is burning-red.
B. Statements C and E are not both true and not both false.
C. Statements A and E are not both true and not both false, and the moon is blue.
D. Statement A is false, and the moon is (as everyone knows) made of green cheese.
E. Statement B is false, and either the moon is yellow or the moon is not yellow.

What color is the moon?

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  • 2
    $\begingroup$ my logic fuse just got burnt... $\endgroup$ – OutFall Feb 16 '15 at 23:52
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    $\begingroup$ I think your "Each of the following five statements is either true or false" is ambiguous. Here's why. Let's say that A = "The sky is blue". The statement "The sky is blue and the moon is made of green cheese" is false. Now let's say that A = "The sky is green." The statement "The sky is green and the moon is made of green cheese" is also false. Therefore, nothing can be inferred about the truth value of A through a determination of the truth value of the statement about the moon. $\endgroup$ – BobRodes Feb 17 '15 at 20:18
  • $\begingroup$ Perhaps "if any part of the following five statements is true, all parts of the statement are true; if any part is false, then all parts are false" would be a clarification. $\endgroup$ – BobRodes Feb 17 '15 at 20:20
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  • The moon is not made of green cheese: D is false.

  • If A is false, then D is false and E is true and the moon is not burning-red. If E is true, then B is false. Then C and E are either both true or both false, and E true implies C true. Then the moon is BLUE.

  • If A is true and the moon is not burning red, then E is false. If E is false, then B is true. Then C and E are not both true and not both false, and E false implies C true. Then the moon is BLUE.

  • If A is true and the moon is burning red. Then C is false. IF E is true, then B is false, and C is true, and this contradicts C is false. If E is false, then B is true, and C is true, and this contradicts C is false. No solution here.


Two solutions:

  • A, B, C true and D, E false and the moon is BLUE.
  • A, B, D false and C, E true and the moon is BLUE.

Therefore the moon is always BLUE!

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E simplifies to "B is false".

If E is true, B is false, therefore C is true. If E is false, B is true, and so is C.

Therefore, the moon is always

blue.

(Option 1, "E = true" is also impossible, but that takes a bit more work. This is the lazy way.)

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Let's give it a go, should we?

The moon is

Blue

Because:

A. Statement D is true, or statement E is false, or the moon is burning-red.
B. Statements C and E are not both true and not both false.
C. Statements A and E are not both true and not both false, and the moon is blue.
D. Statement A is false, and the moon is (as everyone knows) made of green cheese.
E. Statement B is false, and either the moon is yellow or the moon is not yellow.

A = D or !E or red
B = (C != E)
C = (A != E) and blue
D = !A and green
E = !B

if E
=> !B
=> C == E
=> C true
=> blue and !A
=> red or D
=> D
=> !A and green

=> !E

if B
=> C true
=> blue and A
=> A => true
=> !D

=> A, B, C, !D, !E and the moon is blue

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