A bijection is a function, but if A is nonempty and |B| > 1, then A x B is not a function. If there is no mistake in the question, then the fact that A x B is a bijection implies that |A| = |B| = 1 or |A| = |B| = 0, so |A| = |B|.
My discrete mathematics course has just started, so I'm not very good even at probably fairly easy things:
Prove if is a bijection between finite sets and then .
It looks pretty obvious because of the nature of this bijection, but I just can't seem to figure out notations to prove it in a mathematical way.