Quoting my text book:
Two random variables $X_{1},X_{2}$ are called independent, if:
$P(X_{1}\in A_{1}, X_{2}\in A_{2}) = P(X_{1}\in A_{1})\cdot P(X_{2}\in A_{2})$
for all $A_{1},A_{2}$ where $A_{i}$ is a subset of $\mathbb{R}$.
The 'if' in the above text confuses me.
If you have two independent variables and want to find $P(X_{1}\in A_{1}, X_{2}\in A)$ can you then just find the product of $P(X_{1}\in A_{1})$ and $P(X_{2}\in A_{2})$?