Question

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

• A. $A\cap B$
• B. $A\cup B$
• C. $\varphi$
• D. none of these

Answer 1

The correct option is C $\varphi$

Given $A,B$ are disjoint sets then

$A\cap B=\varphi$......(1).

Now,

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

$=(A\cap A^{\prime })\cup (A\cap B)$ [ By Distributive Property ]

$=\varphi \cup \varphi$ [ Using (1) and by property ]

$=\varphi$.