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 $C\cup A$

The union $C\cup A$ is the set of all elements that are in $C$ or in $A$ or in both. On the Venn - diagram, this is the region covered by both circles $C$ and $A$ (including their intersection).

Step2: Find $(C\cup A)'$

The complement $(C\cup A)'$ is the set of all elements in the universal set $U$ that are not in $C\cup A$. So, we shade the region outside of the circles $C$ and $A$ in the Venn - diagram.

Step3: Find $(C\cup A)'\cap B$

The intersection $(C\cup A)'\cap B$ is the set of all elements that are in both $(C\cup A)'$ and $B$. So, we shade the part of circle $B$ that is outside of circles $C$ and $A$.

Answer:

Shade the part of circle $B$ that is outside of circles $C$ and $A$.