If N a = { a n : n ∈ N } , then N 3 ∩ N 4 = Options: A . &nbsp N 7 B . &nbsp N 12 C . &nbsp N 3 D . &nbsp N 4

Answer: Option B : B N a = { a n : n ∈ N } N 3 ∩ N 4 = { 3 , 6 , 9 , 12 , 15 … … } ∩ { 4 , 8 , 12 , 16 , 20 , … … } = { 12 , 24 , 36 … … } = N 12 [ ∵ 3,4 are relatively prime numbers ] ∴ N 3 ∩ N 4 = N 12

If Na={an:n∈N} , then N3∩N4 =

Question

If $N_{a} = {a n : n \in N}$ , then $N_{3} \cap N_{4}$ =

Options:

A .

N_{7}

B .

N_{12}

C .

N_{3}

D .

N_{4}

Answer: Option B
:
B

$N_{a} = {a n : n \in N}$
$N_{3} \cap N_{4} = {3, 6, 9, 12, 15 \dots \dots} \cap {4, 8, 12, 16, 20, \dots \dots}$

$= {12, 24, 36 \dots \dots} = N_{12}$

[ $∵$ 3,4 are relatively prime numbers ]
$∴$ $N_{3} \cap N_{4}$ = $N_{12}$

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