Question

If aN = {ax/x ∈ N} and bN ∩ cN = dN Where b, c ∈ N are relatively prime then 

(a) d = bc 

(b) c = bd 

(c) b = cd 

(d) a = bd

Answer 1

The correct option (a) d = bc

Explanation:

bN = {bx/x ∈ N} = the set of positive integer multiples of b 

cN = {cx/x ∈ N} = the set of positive integer multiples of c 

∴ bn ∩ cN = the set of positive integer multiples of bc = bcN [∵ b and c are prime] Hence d = bc