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 $A'$

$A'$ is the complement of set $A$, which includes all elements in $U$ that are not in $A$. Shade the region outside of circle $A$ in the Venn - diagram.

Step2: Find $B'$

$B'$ is the complement of set $B$, which includes all elements in $U$ that are not in $B$. Shade the region outside of circle $B$ in the Venn - diagram.

Step3: Find $A'\cap B'$

$A'\cap B'$ is the intersection of $A'$ and $B'$, so it is the region that is outside both $A$ and $B$. This is the region in $U$ that is outside of both circle $A$ and circle $B$.

Step4: Find $C\cup(A'\cap B')$

$C\cup(A'\cap B')$ is the union of set $C$ and $A'\cap B'$. So, shade all of the region inside circle $C$ and also the region that is outside both $A$ and $B$.

Answer:

Shade all of circle $C$ and the region in $U$ that is outside both circle $A$ and circle $B$.