Question

the venn diagram shows sets a, b, c, and the universal set u. shade c ∩ (a ∪ b) on the venn diagram.

Explanation:

Step1: Find \(A'\) and \(B'\)

\(A'\) is the region outside of set \(A\) in the universal - set \(U\), and \(B'\) is the region outside of set \(B\) in the universal - set \(U\). Then \(A'\cup B'\) is the region that is either outside of \(A\) or outside of \(B\) (or both), which includes the parts of \(U\) that are not in \(A\cap B\).

Step2: Find \(C\cap(A'\cup B')\)

We need to find the intersection of set \(C\) and the region \(A'\cup B'\). So we shade the part of set \(C\) that is not in \(A\cap B\).

Answer:

Shade the part of circle \(C\) that is not in the intersection of \(A\) and \(B\). This includes the parts of \(C\) that are outside of \(A\) and outside of \(B\), as well as the part of \(C\) that is only in \(A\) or only in \(B\) (but not in \(A\cap B\)).