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If aN = {ax:x in N} and bNnncN=dN,whereb...

If `aN = {ax:x in N} and bNnncN=dN,`where`b,cin N` are relatively prime, then show that `d=bc`.

A

d = bc

B

c = bd

C

b = cd

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
A
bN = The set of positive integral multiples of b
cN = The set of positive integral multiples of c
`therefore bNnncN` = The set of positive integral multiples of bc
= bc N [`because` b and c are prime]
`therefore d = bc`
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