Question

a = {3, 5, 6, 9} b = {2, 5, 7, 9} c = {x ∈ z | x is composite} d = {x ∈ z | x is a multiple of 2} (d ∪ b) ∩ a = {ex: 10, 11, 12, 13, 14} (a ∩ c) ∪ b = {}

Explanation:

Step1: List out elements of sets

$A = \{3,5,6,9\}$, $B=\{2,5,7,9\}$, $C=\{x\in\mathbb{Z}\mid x\text{ is composite}\}=\{4,6,8,9,10,12,14,\cdots\}$, $D = \{x\in\mathbb{Z}\mid x\text{ is a multiple of }2\}=\{ \cdots,- 4,-2,0,2,4,6,\cdots\}$.

Step2: Calculate $(A\cap C)$

$A\cap C=\{6,9\}$ (common elements of $A$ and $C$).

Step3: Calculate $(A\cap C)\cup B$

$(A\cap C)\cup B=\{2,5,6,7,9\}$ (combine elements of $A\cap C$ and $B$).

Answer:

$\{2,5,6,7,9\}$