First slide

Operations on Sets

Question

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

Moderate

A

b=cd
B

c=bd
C

d= bc
D

None of these

Solution

Given that,
$\begin{array}{l} aN = {an : n \in N} \\ bN = {bn : n \in N} and cN = {cn : n \in N} \end{array}$
Also given,
$\begin{array}{l} bN \cap cN = dN \\ bc \in bN \cap cN or bc \in dN \\ bc = d \end{array} [∵ b and c are coprime]$
[ coprime numbers are those numbers, whose common factor is 1. e.g., (i) 3 and 5 (ii) 5 and 9 etc.]

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