Question

If $A\cap B$ = $\varphi$, then $A^{{}^{\prime }}$$\cup$ B${}^{{}^{\prime }}$ = $\xi$(Universal Set). If true enter 1 else 0.

Answer 1

Since, $A\cap B=\varphi$, so that sets A and B are disjoint sets with no elements in common.
Now, $A^{{}^{\prime }}$ will be the region outside A and it will be include B as well.
And $B^{{}^{\prime }}$ will be the region outside B and it will be include A as well.
So, $A^{{}^{\prime }}\cup B^{{}^{\prime }}$ will be the combination of these two regions, which in other words is the complete region $\xi$