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As i understand, it is implied that numbers a and b must be integer(otherwise, the statement is false). So, this numbers can be even or odd. There are 4 possibilities:
1).a, b are both even
2).a, b are both odd
3).a is even, b is odd
4).a is odd, b is even
Firstly we will examine (2) condition: a and b are both odd means , where n and k both
4nk and 2(n+k) are both even, then their sum is even, then their sum plus 1 is odd. ab is odd.
We considered (2) situation and came to conclusion that: (ab is odd). That means: (ab is odd)
(ab is odd) means (ab is even)
(ab is even) .
So, if ab is even than at least one of the two numbers is even
Statement has been proven