If a∈N, where aN={ax:x∈N} , then the 3N∩7N is

3N={3x:x∈N}={3,6,9,12,15,18,21,⋯}7N={7x:x∈N}={7,14,21,28,⋯}3N∩7N={21,42,⋯}=21N

If a∈N, where aN={ax:x∈N} , then the 3N∩7N is

3N={3x:x∈N}={3,6,9,12,15,18,21,⋯}7N={7x:x∈N}={7,14,21,28,⋯}3N∩7N={21,42,⋯}=21N

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If $a \in N$ , where $a N = {a x : x \in N}$ , then the $3 N \cap 7 N$ is

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$21 N$

$12 N$

$3 N$

$7 N$

answer is A.

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Detailed Solution

$3 N = {3 x : x \in N} = {3, 6, 9, 12, 15, 18, 21, \dots}$

$7 N = {7 x : x \in N} = {7, 14, 21, 28, \dots}$

$3 N \cap 7 N = {21, 42, \dots}$

$= 21 N$

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If a∈N, where aN={ax:x∈N} , then the 3N∩7N is

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If $a \in N$ , where $a N = {a x : x \in N}$ , then the $3 N \cap 7 N$ is