Let $x$ and $y$ be integers. Write a proof by contraposition to show that "if $x+y$ is even, then $x$ and $y$ have the same parity."
proof by contrapositive:
Usually i would start these and assume the negation of the if statement, then i would list a definition and use it to substitute the then statement but that's not possible in this sentence.
Assume $x+y$ is odd
by definition of odd $∃k∈ℤ$ such that $x=2k+1$
by definition of odd $∃j∈ℤ$ such that $y=2j+1$
it's obvious that they must have the same parity to stay odd but i don't know how to exactly write it in proof form.