Question

If $aN=\{ax:x\in N\}$, describe the set $3N\cap 7N$.

Answer 1

Ans. $21N.$
According to the given notation,
$3N=\{3x:x\in R\}=\{3,6,9,\mathrm{12.......}\}$
and $7N=\{7x:x\in R\}=\{7,14,21,28,35,42,.......\}$
Hence $3N\cap 7N=\{21,42,63\}$
$=\{21x:x\in N\}=21N$