Question

If $N_a=\left[an:n\in N\right]$, then $N_5\cap N_7$ is equal to

• A. $N_7$
• B. $N$
• C. $N_{35}$
• D. $N_5$

Answer 1

The correct option is C

$N_{35}$

Explanation for the correct option

Given: $N_a=\left[an:n\in N\right]$

$$\begin{gathered} \therefore N_5=\left[5n:n\in N\right] \\ \Rightarrow N_5=\left[5,10,15.20,25,30,35,40m45,50,55,60,65,70,75,80,85.........\right] \\ \therefore N_7=\left[7n:n\in N\right] \\ \Rightarrow N_7=\left[7,14,21,28,35,42,49,56,63,70,77......\right] \end{gathered}$$

Thus the value of $N_5\cap N_7$ is,

$\begin{array}{rcl}\left(N_5\cap N_7\right)& =& \left[35,70,105,.......\right]\\ & =& \left[\left(1\right)35,\left(2\right)35,\left(3\right)35,........\right]\\ & =& N_{35}\end{array}$ $\left[\because N_a=\left[an:n\in N\right]\right]$

Hence, option(C) i.e. $N_{35}$ is the correct option.