Question

Let $A,B$ be two disjoint sets then $A\cap (A^{\prime }\cup B)=$

Answer 1

Given $A,B$ are two disjoint sets then $A\cap B=\varphi$......(1).

Now,

$A\cap (A^{\prime }\cup B)$

$=(A\cap A^{\prime })\cup (A\cap B)$

$=\varphi \cup \varphi$ [ Using (1) and since $A\cap A^{\prime }=\varphi$]

$=\varphi$.