If aN = { ax : x in N },then the set 3N cap 7 | vedclass

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(A) Given $aN = \{ ax : x \in N \}$.$3N = \{ x \in N : x 	ext{ is a multiple of } 3 \}$.$7N = \{ x \in N : x 	ext{ is a multiple of } 7 \}$.$3N \cap

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$21N$

Vedclass · Answer

(A) Given $aN = \{ ax : x \in N \}$.$3N = \{ x \in N : x 	ext{ is a multiple of } 3 \}$.$7N = \{ x \in N : x 	ext{ is a multiple of } 7 \}$.$3N \cap 7N$ represents the set of all natural numbers that are multiples of both $3$ and $7$.Since $3$ and $7$ are coprime,their least common multiple is $3 	imes 7 = 21$.Therefore,$3N \cap 7N = \{ x \in N : x 	ext{ is a multiple of } 21 \} = 21N$.

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

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