Question: If aN = {ax: x $\in$ N} and bN $\cap$ cN = dN, where b,c $\in$ N are relatively prime then, A...

Question

If 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. None of these.

Answer 1

Solution

Hint: Two numbers can be relatively prime when they have no common factors other than 1. In other words there is no value that you could divide them both by exactly (without any remainder).

Complete answer:

Since b and c relatively prime,

$\Rightarrow$ bN $\cap$ cN = dN

$\Rightarrow$ (bc) N = dN

$\Rightarrow$ bc = d

So, option A is correct.

NOTE: - In case b and c were not relatively prime but any numbers belonging to N then the corresponding answer would be None of these.

Question: If aN = {ax: x \(\in\) N} and bN \(\cap\) cN = dN, where b,c \(\in\) N are relatively prime then, A...

Solution