Is there a way to prove/create (or are there known hash functions) two hash functions that never have the same collision? I mean, like provable in way that someone who took one cryptography class in university can prove.

For example, I want hash functions $A$ and $B$ such that if hash function $A$ collides on $X$ and $Y$, then $B$ will not collide on these $X$ and $Y$:

$$A(X) = A(Y) \quad \Rightarrow \quad B(X) \neq B(Y) $$