Question

For any two sets $A$ and $B,$ $A-(A\cap B)$ = ___.

• A. $A^{\prime }\cap B$
• B. $A\cap B^{\prime }$
• C. $A^{\prime }\cap B^{\prime }$
• D. $(A\cup B{)}^{\prime }$

Answer 1

The correct option is B $A\cap B^{\prime }$

$A-(A\cap B)=A\cap {(A\cap B)}^{\prime }=A\cap (A^{\prime }\cup B^{\prime })[\because \text{de-Morgan's law}]=(A\cap A^{\prime })\cup (A\cap B^{\prime })\left[\text{Distributive property}\right]=\varphi \cup (A\cap B^{\prime })[\because A\cap A^{\prime }=\varphi ]=A\cap B^{\prime }[\because C\cup \varphi =C]$