Question

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

• A. 21 N
• B. 10 N
• C. 4 N
• D. None

Answer 1

Answer: (A)

We have,
$3N=\{3x:x\in N\}=\{3,6,9,12,15,18,21,24\dots ..\}$
$=\{x\in N:x$ is a multiple of $3\}$
and $7N=\{7x:x\in N\}=\{7,14,21,28\dots \dots \}$
$=\{x\in N:x$ is a multiple of 7$\}$
$\therefore 3N\cap 7N=\{x\in N:x$ is a multiple of 3 and 7$\}$
$=\{x\in N:x$ is a multiple of $21\}$
$=\{21,42,\dots \dots \}=21N$