Question

Suppose $U=\{1,2,3,4,5,6,7,8,9\},A=\{1,2,3,4\}$ and $B=\{2,4,6,8\}$. How $(A\cup B{)}^{\prime }$ is related to $A^{\prime }$ and $B^{\prime }$? What relation you see between $(A\cap B{)}^{\prime }$ and $A^{\prime }$ and $B^{\prime }$?

Answer 1

$U=\{1,2,3,4,5,6,7,8,9,\}$

$A=\{1,2,3,4\}$

$B=\{2,4,6,8\}$

$A\cup B=\{1,2,3,4,6,8\}$

${(A\cup B)}^{{}^{\prime }}=\{5,7,9\}$

$A^{{}^{\prime }}=\{5,6,7,8,9\}$

$B^{{}^{\prime }}=\{1,3,5,7,9\}$

$A^{{}^{\prime }}\cap B^{{}^{\prime }}=\{5,7,9\}$

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

$A\cap B=\{2,4\}$

${(A\cap B)}^{{}^{\prime }}=\{1,3,5,6,7,8,9\}$

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