Question

If $aN=(an:n\in N)$ and $bN\cap cN=dN$, where $a,b,c\in N$ and $b,c$ are coprime, then

• A. $b=cd$
• B. $c=bd$
• C. $d=bc$
• D. None of these

Answer 1

The correct option is C $d=bc$

Given : $aN=(an:n\in N)$ and $bN\cap cN=dN$, where $a,b,c\in N$ and $b,c$ are coprime

We have,

$bN=(bn:n\in N)$, $cN=(cn:n\in N)$

and $dN=(dn:n\in N)$

Also, $bc\in bN\cap cN=dN$

$\therefore$ $bc=d$ ..... $[\because b,c$ are coprime$]$.