Question

a = {4, 5, 8, 9}, b = {2, 3, 5, 8}, c = {x ∈ z | x is a multiple of 3}, d = {x ∈ z | x is composite}, (b ∩ c) ∪ a = {ex: 10, 11, 12, 13, 14}, a ∩ (d ∪ b) = {}

Explanation:

Step1: List elements of sets

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

Step2: Find $D\cup B$

$D\cup B$ is the set of elements that are in $D$ or $B$. So $D\cup B=\{2,3,4,5,6,8,9,\cdots\}$

Step3: Find $A\cap(D\cup B)$

$A\cap(D\cup B)$ is the set of elements that are in both $A$ and $D\cup B$. So $A\cap(D\cup B)=\{4,5,8,9\}$

Answer:

$\{4,5,8,9\}$