Investigate!
Decide which of the following are valid proofs of the following statement:
-
Suppose
and are odd. That is, and for some integers and ThenTherefore is odd. -
Assume that
or is even - say it is (the case where is even will be identical). That is, for some integer ThenThus is even. -
Suppose that
is even but and are both odd. Namely, and for some integers and ThenBut since is an integer, this says that the integer is equal to a non-integer, which is impossible. -
Let
be an even number, say and be an odd number, sayTherefore must be even.