Question

shade the area or areas of the venn diagram that represent $(a \cap b)$.

Explanation:

First, identify $A \cap B$: this is the overlapping region of circles A and B, containing the numbers 1 and 2. The complement $(A \cap B)'$ includes all elements in the universal set $U$ that are NOT in $A \cap B$. This means we shade the parts of circle A not overlapping with B (numbers 4, 11, 15), the parts of circle B not overlapping with A (numbers 7, 5), and the area inside the universal set but outside both circles (numbers 10, 12, 13).

Answer:

Shade the following regions:

1. The non-overlapping part of circle A (containing 4, 11, 15)
2. The non-overlapping part of circle B (containing 7, 5)
3. The area inside the universal set $U$ outside both circles (containing 10, 12, 13)

Leave the overlapping region of A and B (containing 1, 2) unshaded.