Questions: Sketch a Venn diagram like the one shown to the right, and use shading to show the set C' ∩ (A' ∪ B).

Transcript text: Sketch a Venn diagram like the one shown to the right, and use shading to show the set $C^{\prime} \cap\left(A^{\prime} \cup B\right)$.

Solution

Solution Steps

Step 1: Find A'∪B

A' is the complement of A, meaning everything outside of A. A'∪B is everything in B along with everything outside of A. This includes all of B, the part of C not intersecting A, and the area outside the circles.

Step 2: Find C'∩(A'∪B)

C' is the complement of C, meaning everything outside of C. C'∩(A'∪B) is the intersection of everything outside C and everything we shaded in the previous step. This leaves just the portion of B not intersecting C and the area outside the circles.

Step 3: Select the correct Venn Diagram

The Venn diagram which represents C'∩(A'∪B) is option D, which shows the area of B not intersecting C and the area outside all three circles shaded.