Question

If $A=\{1,3,5,7,9,11,13,15,17\},B=\{2,4,....,18\}$ and N is the universal set, then $A^{\prime }\cup ((A\cup B)\cap B^{\prime })$

• A. A
• B. N
• C. B
• D. R

Answer 1

The correct option is B N

$A=\{1,3,5,7,9,11,13,15,17\}$

$A^{\prime }=N-A=N-\{1,3,5,7,9,11,13,15,17\}=\{2,4,6,8,10,12,14,16,18\}$

$A\cup B=\{1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18\}$

$B^{\prime }=N-B=N-\{2,4,6,8,10,12,14,16,18\}=\{1,3,5,7,9,11,13,15,17\}$

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

$=\{1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18\}\cap \{1,3,5,7,9,11,13,15,17\}$

$=\{1,3,5,7,9,11,13,15,17\}$

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

$=\{2,4,6,8,10,12,14,16,18\}\cup \{1,3,5,7,9,11,13,15,17\}$

$=\{1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18\}=N$