Question

each venn diagram has sets a, b, and the universal set u. (a) shade ( a cap b ). (b) shade ( a cup b ).

Explanation:

Step1: Define complement of A

$A'$ is all elements in $U$ not in $A$.

Step2: Find intersection with B

$A' \cap B$ is the part of $B$ not overlapping with $A$.

Step3: Define complement of B

$B'$ is all elements in $U$ not in $B$.

Step4: Find union with A

$A \cup B'$ is all of $A$ plus the part of $U$ not in $B$.

Answer:

(a) Shade the region of circle B that does not overlap with circle A (the exclusive part of B).
(b) Shade the entire circle A, plus the area inside the universal set U that is outside of circle B (including the area outside both A and B).

Visual Representation Summary:

Part (a)	Part (b)