Question

If the universal set, $\in \{1,2,3,4,5,6,7,8\}$; A = {even numbers}, B = {odd numbers} , C = {2, 5, 6, 7, 8} , Find :
i) $A\cup B$ ii) $A^{\prime }\cap B^{\prime }$

Answer 1

Given universal set $\in =\{1,2,3,4,5,6,7,8\}$

$A=\left\{\text{even numbers}\right\}=\{2,4,6,8\}$

$B=\left\{\text{odd numbers}\right\}=\{1,3,5,7\}$

$C=\{2,5,6,7,8\}$

i) $A\cup B=\{2,4,6,8\}\cup \{1,3,5,7\}=\{1,2,3,4,5,6,7,8\}=\in$

ii) $A^{\prime }\cap B^{\prime }=(A\cup B{)}^{\prime }={\in }^{{}^{\prime }}=\varphi (emptyset)$