Prove that

Let $x$ be some element in set $A-B$ that is $x \in(A-B)$

Now if we prove that $x \in\left(A \cap B^{\prime}\right)$ then $(A-B)=\left(A \cap B^{\prime}\right)$

$x \in(A-B)$ means $x \in A$ and $x \notin B$

Now $x \notin B$ means $x \in B$.'

Hence we can say that $x \in A$ and $x \in B$.'

Hence $x \in A \cap B$.'

And as $x \in A \cap B^{\prime}$ and also $x \in A-B$ we can conclude that $A-B=A \cap B .^{\prime}$