Question

In $aN=\{ax:x\in N\}$ and $bn\cap cN=dN$, where $b,c\in N$ are relatively prime, then

• A. $d=bc$
• B. $c=bd$
• C. $b=cd$
• D. $Noneofthese$

Answer 1

The correct option is A $d=bc$

Since $b$ and $c$ are relatively prime, therefore $bN\cap cN=dN\Rightarrow \left(bc\right)N=dN\Rightarrow bc=d.$

Note. In case $b$ and $c$ were not relatively prime but any numbers belonging to $N$, then the corresponding answer would be $\left(d\right).$