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Q.
If $aN =\{ ax : x \in N \}$, then the set $3 N \cap 7 N$ is
Sets
Solution:
We have,
$3 N =\{3 x : x \in N \}=\{3,6,9,12,15,18,21,24 \ldots . .\} $
$=\{ x \in N : x$ is a multiple of $3\}$
and $7 N =\{7 x : x \in N \}=\{7,14,21,28 \ldots \ldots\}$
$=\{ x \in N : x$ is a multiple of 7$\}$
$\therefore 3 N \cap 7 N =\{ x \in N : x$ is a multiple of 3 and 7$\}$
$=\{x \in N: x$ is a multiple of $21\}$
$=\{21,42, \ldots \ldots\}=21 \,N$