Question

(a) shade $(a cup b)$. (b) shade $a cap b$. try again the sets $(a cup b)$ and $a cap b$ equal? $circ$ yes $circ$ no

Explanation:

Step1: Solve part (a) using De Morgan's Law

First, apply De Morgan's Law: $(A \cup B')' = A' \cap B$. This means the region is the part of set $B$ that does not overlap with $A$.

Step2: Shade region for (a)

Shade the portion of circle $B$ that is outside circle $A$ (the non-overlapping part of $B$), and exclude all of $A$ and the universal set outside $B$.

Step3: Solve part (b) directly

$A \cap B'$ is the part of set $A$ that does not overlap with $B$.

Step4: Shade region for (b)

Shade the portion of circle $A$ that is outside circle $B$ (the non-overlapping part of $A$), and exclude all of $B$ and the universal set outside $A$.

Step5: Compare the two sets

The set $(A \cup B')' = A' \cap B$, which is the non-overlapping part of $B$. The set $A \cap B'$ is the non-overlapping part of $A$. These are not the same region.

Answer:

(a) Shade the non-overlapping portion of circle $B$ (the part of $B$ not inside $A$)
(b) Shade the non-overlapping portion of circle $A$ (the part of $A$ not inside $B$)
For the final question: No