$H$ is a family of weakly universal hash functions if for two elements $x,y$:
$$ P(h(x) = h(y)) \le \frac1m, $$
where $m$ is the size of the domain, and $h$ is chosen at random from $H$.
Given a hash family, how could one prove that it is weakly universal. I understand how to prove it isn't (proof by counter-example) but I cannot find any examples for when it is.
I apologise if this is a duplicate of another question. I was not able to find any examples online specifically for weakly universal hash functions.