Question

in the venn diagram below, a and c are events in the sample space s. (note: for any event x, we use $overline{x}$ to denote
ot x.\) (a) shade a ∪ c. (b) shade a ∩ c.

Explanation:

Step1: Recall union definition

The union $A\cup C$ consists of all elements that are in $A$ or in $C$ (or in both). So, shade all of circle $A$, all of circle $C$, including the overlapping part.

Step2: Recall intersection definition

The intersection $A\cap C$ consists of all elements that are in both $A$ and $C$. So, shade only the overlapping part of circle $A$ and circle $C$.

Answer:

(a) Shade all of circle $A$, all of circle $C$ (including the overlap).
(b) Shade only the overlapping part of circle $A$ and circle $C$.