AmodY = X1
BmodY = X2
(X1+X2)modY = X3 = CmodY.
Where C = A+B, and Y is a set $\mathbb{R}$eal number
I was working my way through an exam, and had to prove a simple 2 evens or 2 odds added together equal an even, and this was the completely off the wall over-engineered solution I came up with, opposed to using the "boring" x=2a y=2b way, which I know to be true within the context of the exam question. However I suck at proofs, and am unsure if my off the wall way of solving the problem is actually true, it works in this case and I haven't been able to find a case where it is disproven, but I don't know how to prove (or disprove) a statement like this, so I can use it over the x=2a y=2b way.