Basic set theory proof about cardinality of cartesian product of two finite sets I'm really lost on how to do this proof:
If $S$ and $T$ are finite sets, show that $|S\times T| = |S|\times |T|$.
(where $|S|$ denotes the number of elements in the set)
I understand why it is true, I just can't seem to figure out how to prove it.
Any hints/help will be greatly appreciated!

I would use a combinatorial argument. Note that $S \times T = \{ (s, t) : s \in S, t \in T \}$. So how many options are there for $s$? We choose one from $|S|$, giving us $|S|$ such options. Then for the $t$ element, there are $\binom{|T|}{1} = |T|$ option. Choosing $s$ and $t$ are done independently, so by rule of product, we multiply: $|S| \cdot |T|$. And so $|S \times T| = |S| \cdot |T|$. 
