Question:
Let $A=\{x: x \in N, x$ is a multiple of 3$\}$ and $B=\{x: x \in N$ and $x$ is a multiple of 5$\}$. Write $A \cap B$.
Solution:
A = {x:x ∈ N and x is a multiple of 3.}
= {3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45,...}
B = {x:x ∈ N and x is a multiple of 5.}
={5, 10, 15, 20, 25, 30, 35, 40, 45,...}
Thus, we have:
$A \cap B=\{15,30,45, \ldots\}$
$=\{x: x \in N$, where $x$ is a multiple of $15 .\}$