Let $A = {x : x$ is a multiple of $3}$ and $B = {x : x$ is a multiple of $5}$ Then $A \cap B$ is given.

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Solution

$A = x : x$ is a multiple of $3$

$\Rightarrow A = {0, 3, 6, 9, 12, 15.....}$

$B = x : {x$ is a multiple of $5}$

$\Rightarrow B = {0, 5, 10, 15, 20, 25, 30....}$

$A \cap B = {0, 15, 30.....}$

$∴ A \cap B = {x : x$ is a multiple of $15}$

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