Question

challenge activity 3.4.2: set operations with three sets. 664492.4002982.qx3zqy7 jump to level 1 select the region(s) of: $overline{a}$ select the region(s) of: $(b - c)-a$

Explanation:

Step1: Recall set - complement definition

The complement of set \(A\), denoted as \(\overline{A}\), consists of all elements in the universal set \(U\) that are not in \(A\). In a Venn - diagram, for the first problem with two sets \(A\) and \(B\) in a universal set \(U\), the region of \(\overline{A}\) is the part of the universal set that is outside of circle \(A\). This includes the non - overlapping part of \(B\) and the part of \(U\) that is outside of both \(A\) and \(B\).

Step2: Recall set - difference definition

For the second problem, \(B - C\) is the set of elements that are in \(B\) but not in \(C\). In the Venn - diagram of three sets \(A\), \(B\), and \(C\), \(B - C\) is the part of circle \(B\) that does not overlap with circle \(C\). Then, \((B - C)-A\) is the part of \(B - C\) that is not in \(A\). So we first find \(B - C\) (elements in \(B\) but not \(C\)) and then remove the elements of \(A\) from it.

Answer:

For the first problem (\(\overline{A}\)): The region is the part of the universal set outside of circle \(A\) (the non - overlapping part of \(B\) and the part of \(U\) outside both \(A\) and \(B\)).
For the second problem \((B - C)-A\): First, find the part of \(B\) that does not overlap with \(C\), and then from that region, remove the part that overlaps with \(A\).