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.\) shade $overline{c}cupoverline{d}$ on the venn diagram.

Explanation:

Step1: Recall set - complement definition

$\overline{C}$ is the set of all elements in the sample - space $S$ that are not in $C$, and $\overline{D}$ is the set of all elements in the sample - space $S$ that are not in $D$.

Step2: Recall set - union definition

The union $\overline{C}\cup\overline{D}$ is the set of all elements that are in $\overline{C}$ or in $\overline{D}$ (or in both).
To shade $\overline{C}\cup\overline{D}$ on the Venn - diagram:

1. First, shade the region outside of circle $C$ (this is $\overline{C}$).
2. Then, shade the region outside of circle $D$ (this is $\overline{D}$). The combined shaded region is $\overline{C}\cup\overline{D}$. In other words, the only part of the Venn - diagram that should not be shaded is the intersection $C\cap D$.

Answer:

Shade the entire sample - space $S$ except for the intersection region of $C$ and $D$.