Question

refer to the accompanying figure, and list the points that belong to each set. (enter your answer using roster notation. enter ∅ for the empty set.) (a) a ∩ (b ∪ c) (b) (b ∩ c)^c

Explanation:

Step1: Identify sets from the figure

• Set $A = \{u, v, r, y\}$
• Set $B = \{x, v, r, w\}$
• Set $C = \{w, r, u, z\}$
• Universal set $U = \{t, x, v, r, w, u, y, z, s\}$

Step2: Solve part (a): Find $B \cup C$

Combine all unique points in $B$ and $C$:
$B \cup C = \{x, v, r, w, u, z\}$

Step3: Solve part (a): Find $A \cap (B \cup C)$

Find common points in $A$ and $B \cup C$:
$A \cap (B \cup C) = \{u, v, r\}$

Step4: Solve part (b): Find $B \cap C$

Find common points in $B$ and $C$:
$B \cap C = \{r, w\}$

Step5: Solve part (b): Find $(B \cap C)^c$

Find all points in $U$ not in $B \cap C$:
$(B \cap C)^c = \{t, x, v, u, y, z, s\}$

Answer:

(a) $\{u, v, r\}$
(b) $\{t, x, v, u, y, z, s\}$