If $x$ is even and $y$ is odd, then $x+y$ is even.

Question

I was also asked to proof if I say the above statement is true and give a counter example if I say it is False.

Moreover, I prefer the statement to be false because the sum of any even and odd number will always be odd. e.g. $4+3=7$ is odd.

Is my reason correct or is there a law to prove that it is true or disprove it to show that it is false?

Answer 1

Apart from a counter example you can also try to prove this statement as follows:

Let x be of the form $2k$, where $k\in \mathbb Z$ and y be of the form $2p+1$, where $p\in \mathbb Z$. Then their sum will of the form $2(p+k)+1$=$2K+1$, where $K \in \mathbb Z$. This is definitely odd.