# Math Help - How to prove distributivity of cardinals?

1. ## How to prove distributivity of cardinals?

I have this kind of problem:
(1): Let k,m,l be cardinals. Prove that k(m+l)=km+lm.

I know, that I have to prove that there exist a bijection between Kx(LuM) and
(KxL)u(KxM) where card(K) = k, card(L) = l and card(M) = m, but how I do it?
I'm little bit lost here, can anyone help?

2. Pick representative sets K, L and M, respectively (all mutually disjoint). You want to show that K×(LM) ∼ (K×L)∪(K×M).
These are actually equal since if (a,b) is in the LHS then either bL or b ∈ M. In the first case, (a,b) ∈ K×L and in the second (a,b) ∈ K×M.
The converse also applies.