Question

complete parts (a) and (b) below for the following set. \\( \bar{d} \cap \bar{k} \\) \\( \mathbf{a.} \\) shade the portion of the venn diagram that represents the given set. use the graphing tool to graph the intersection. click to enlarge graph venn diagram with circles d, k and universal set u

Explanation:

Step1: Understand the Set Operation

The set is \(\bar{D} \cap \bar{K}\), which by De Morgan's Law is equivalent to \(\overline{D \cup K}\) (the complement of the union of \(D\) and \(K\)). This represents the region outside both circles \(D\) and \(K\) in the Venn diagram.

Step2: Identify the Region

In the Venn diagram with universal set \(U\) (the rectangle), circles \(D\) and \(K\), the region for \(\bar{D} \cap \bar{K}\) is the area inside the rectangle but outside both \(D\) and \(K\). So we shade the part of the rectangle not overlapping with \(D\) or \(K\).

Answer:

To solve part (a), shade the region inside the universal set (rectangle) that is outside both circle \(D\) and circle \(K\) (the area not in \(D\) and not in \(K\)). For the graphing tool, this would be the portion of the rectangle not covered by either circle.