Let A = {x : x ∈ N, x is a multiple of 3}
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:

= {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 $15 .\}$

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