Question

For two sets $A,B$ (subsets of $U$),if $A\cap B=\varphi$ then find $A^{\prime }\cup B^{\prime }$. Where $A^{\prime }$ is the complement of the set $A$.

Answer 1

Given for two sets $A,B$, $A\cap B=\varphi$.....(1).

We have from De Morgan's law,

$A^{\prime }\cup B^{\prime }=(A\cap B{)}^{\prime }=(\varphi {)}^{\prime }=U$ [ Using (1)]