Question

If U = {0, 1, 2, 3, 4, 5, 6}, A = {5, 0}, B = {1, 2, 4, 3} then prove $(A\cap B{)}^{{}^{\prime }}=A^{{}^{\prime }}\cup B^{{}^{\prime }}$

Answer 1

$A\bigcap B=\varphi A\bigcup B=\{0,1,2,3,4,5\}$
${(A\bigcap B)}^{{}^{\prime }}=\{2,3,4,6\}$
$A^{{}^{\prime }}=\{2,3,4,6\},B^{{}^{\prime }}=\left\{6\right\}$
$A^{{}^{\prime }}\bigcup B^{{}^{\prime }}=\{2,3,4,6\}$
$\Rightarrow {(A\bigcap B)}^{{}^{\prime }}=A^{{}^{\prime }}\bigcup B^{{}^{\prime }}$ (proved)