Question

You are given that the following set of statements are true. (a) If an integer is even, then it is cosmological. (b) If a real number is cosmological, then it is not mystical. (c) If two real numbers are not mystical, then their product is mystical. Provide a proof by contradiction for the following statement: It is true that at least one of V2 or 18 is mystical.

Answer 1

18 is even, so by rule (a) cosmological, let's call it C. 18 is real and C and so by (b) not mystical, not M.

So V2 which I guess is
`\sqrt 2` is our only hope.

Assume
`\sqrt 2` is not M.

Then
`\sqrt 2 * \sqrt 2 = 2` is M, as by (c) it's the product of two not M numbers.

2 is even, so 2 is C (rule (a)). So 2 is not M (rule (b)). That's a contradiction.

Therefore our assumption is false. We conclude

`\sqrt 2` is mystical.