Question

State, true or false :

If $A$ $\cup$ $B=$ $\xi$, then $A$ ${}^{{}^{\prime }}$$\cap$ $B$ ${}^{{}^{\prime }}$ = $\varphi$

• A. True
• B. False

Answer 1

The correct option is A True

$A^{{}^{\prime }}$ will be the region outside $A$ which will be a part of $B$, since both sets $A$ and $B$ together form the universal set .
And $B^{{}^{\prime }}$ will be the region outside $B$ which will be a part of $A$.
So, $A^{{}^{\prime }}\cap B^{{}^{\prime }}$ will be the intersection of these two regions. Since these regions do not coincide $A^{{}^{\prime }}\cap B^{{}^{\prime }}=\varphi$.