Question

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

Explanation:

Step1: Understand set - notation meaning

$(C\cap B)$ represents the intersection of sets $C$ and $B$, i.e., the elements that are in both $C$ and $B$.

Step2: Understand the union operation

$(C\cap B)\cup A'$ means we take the elements of $(C\cap B)$ and combine them with the elements of the complement of $A$ ($A'$), which are the elements in the universal set $U$ that are not in $A$.

Step3: Shade the regions

1. First, shade the region representing $C\cap B$. This is the overlapping part of circles $C$ and $B$.
2. Then, shade the region representing $A'$. This is the part of the universal - set rectangle that is outside of circle $A$. The final shaded region is the combination of these two shaded regions.

Answer:

Shade the overlapping part of circles $C$ and $B$, and also shade the part of the rectangle outside of circle $A$.