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 ∪ 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 region of the rectangle $S$ that is outside of circle $C$ (but still within the rectangle representing the sample - space).

Since this is a visual task and we can't actually shade in this text - based format, we can describe the shading:

Answer:

(a) Shade the entire area of circle $C$ and circle $D$ (including the overlapping part).
(b) Shade the area of the rectangle $S$ that is outside of circle $C$.