$\alpha \cap \beta = \varnothing$: An Analysis on Set Disjointness

$\alpha \cap \beta = \varnothing$: An Analysis on Set Disjointness



Question: Prove: $A\cap B$ and $A\setminus B$ are disjoint and that
$A=(A\cap B)\cup (A\setminus B)$.



In the above question I would like to know how to come to the desired
conclusion. What is the idea here?