Question

let u = {q, r, s, t, u, v, w, x, y, z}
a = {q, s, u, w, y}
b = {q, s, y, z}
c = {v, w, x, y, z}. list the elements in the set.

1. a ∪ b
2. (a ∪ b)
3. a,

Explanation:

Step1: Find complement of A

$A' = U - A = \{q, r, s, t, u, v, w, x, y, z\} - \{q, s, u, w, y\} = \{r, t, v, x, z\}$

Step2: Solve 14) $A' \cup B$

Combine $A'$ and $B$, remove duplicates:
$A' \cup B = \{r, t, v, x, z\} \cup \{q, s, y, z\} = \{q, r, s, t, v, x, y, z\}$

Step3: Solve 15) $(A \cup B)'$

First find $A \cup B$:
$A \cup B = \{q, s, u, w, y\} \cup \{q, s, y, z\} = \{q, s, u, w, y, z\}$
Then find its complement:
$(A \cup B)' = U - (A \cup B) = \{q, r, s, t, u, v, w, x, y, z\} - \{q, s, u, w, y, z\} = \{r, t, v, x\}$

Step4: Solve 16) $A'$

Result from Step1: $A' = \{r, t, v, x, z\}$

Answer:

1. $\{q, r, s, t, v, x, y, z\}$
2. $\{r, t, v, x\}$
3. $\{r, t, v, x, z\}$