Proof by contrapositive is done by negating the conclusion then
evaluating and directly proving the negation of the original
hypothesis.
Proof by contradiction is done by negating only the conclusion and
proving it the original hypothesis to derive a contradiction.
An example would be for every pair of integers x and y, if x-y is odd,
then x is odd or y is odd.
For proof by contrapositive, we assume x is even and y is even. X = 2i
and Y = 2j, for some integers i and j.
x-y = 2(i-y). Therefore, x-y will always be 2 times an integer.
Therefore, x-y is even, thus proving the contrapositive.
