Given ,
$A\cap B=\phi$ which implies the two sets are disjoint.
Ven diagram of the problem given below:-
$S$ is the universal set .
$A\cup B$ is the set with all the element with $A$ and $B$.
$A\cup {B'}=B'$ as $B’=S-B$ which include $A$ as well so union will be $B’$
$A- {B}=A$ as their intersection is empty set.
So given expression is ,
$(A\cup B)\cap \left ( A\cup B' \right )\cap (A-B)$
=$(A\cup B)\cap B'\cap A$
=$A$
Method 2:-
Universal set $U=\left \{ 1,2,3,4,5,6,7,8,9,10 \right \}$
$A=\left \{ 1,2,3,4 \right \}$
$B=\left \{ 7,8,9,10 \right \}$
$B'=U-B=\left \{ 1,2,3,4,5,6 \right \}$
$A\cup B=\left \{ 1,2,3,4,7,8,9,10 \right \}$
$A\cup B'=\left \{ 1,2,3,4,5,6 \right \}$
$A- B=\left \{ 1,2,3,4 \right \}$
$(A\cup B)\cap \left ( A\cup B' \right )\cap (A-B)$
=$\left \{ 1,2,3,4,7,8,9,10 \right \}\cap \left \{ 1,2,3,4,5,6 \right \}\cap \left \{ 1,2,3,4 \right \}$
$= \left \{ 1,2,3,4 \right \}$
$=A$