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

(a) d = bc 

 aN = {ax/x ∈ N}

 bN = {bx/x ∈ N} = the set of positive integers multiple of b 

 cN = {cx/x ∈ N} = the set of positive integers multiple of c. 

 ∴ bN ∩ cN = the set of positive integers multiple of bc. 

 ∴ bN ∩ cN = bcN(∵ b and c are prime) given – bN ∩ cN = dN 

 hence d = bc.