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 $acap c$. (b) shade $overline{a}$.

Explanation:

Step1: Recall intersection definition

The intersection $A\cap C$ is the set of elements that are in both $A$ and $C$. So, shade the overlapping region of circles $A$ and $C$.

Step2: Recall complement definition

The complement $\overline{A}$ is the set of all elements in the sample - space $S$ that are not in $A$. So, shade the region of the rectangle $S$ that is outside of circle $A$.

Answer:

(a) Shade the overlapping part of circles $A$ and $C$.
(b) Shade the region of the rectangle $S$ that is outside of circle $A$.