Question

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

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

Answer 1

Answer: (B)

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