The dark side of the moon

Question

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?

Answer 1

• 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.

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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!

Answer 2

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.)

Answer 3

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