Question

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

Explanation:

Step1: Find $B\cup C$

The union $B\cup C$ is the set of all elements that are in $B$ or in $C$ (or in both). On the Venn - diagram, this is the region that is covered by either circle $B$ or circle $C$ (including the overlapping part).

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

The complement $(B\cup C)'$ is the set of all elements in the universal set $U$ that are not in $B\cup C$. So, it is the region outside of the combined area of circles $B$ and $C$ within the rectangle $U$.

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

The intersection $A\cap(B\cup C)'$ is the set of all elements that are in both $A$ and $(B\cup C)'$. On the Venn - diagram, shade the part of circle $A$ that is outside of the combined area of circles $B$ and $C$.

Answer:

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