Question

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

Explanation:

Step1: Recall union definition

The union $C\cup D$ consists of all elements that are in $C$ or in $D$ or in both. So, shade the entire region of circle $C$ and circle $D$ including their intersection.

Step2: Recall complement definition

The complement $\overline{C}$ consists of all elements in the sample - space $S$ that are not in $C$. So, shade the entire region of the sample - space $S$ except the region of circle $C$.

Answer:

(a) Shade the entire region of circle $C$ and circle $D$ (including the intersection part).
(b) Shade the region of the sample - space $S$ that is outside of circle $C$.