Question Number 114235 by Aina Samuel Temidayo last updated on 18/Sep/20

Let A={(n,2n):n∈N} and B={(2n,3n):n∈N}. Then A∩B is equal to

Answered by 1549442205PVT last updated on 18/Sep/20

A∩B=(0,0)since (0,0)=(0;2.0)=(2.0;3.0)

Commented byAina Samuel Temidayo last updated on 18/Sep/20

Not correct.

Commented byMJS_new last updated on 18/Sep/20

then what′s correct?

Commented by1549442205PVT last updated on 18/Sep/20

Since N={0,1,2,...},(0,0)can be represented under two forms:(n,2n) and (2n,3n)

Answered by malwaan last updated on 18/Sep/20

(n_1 ,2n_1 )=(2n_2 ,3n_2 ) n_1 =2n_2 2n_1 =3n_2 ⇒n_2 =((2n_1 )/3) ∴ n_1 =2(((2n_1 )/3))=((4n_1 )/3) n_1 (1−(4/3))=0 (−(1/3))n_1 =0⇒n_1 =0⇒n_2 =0 ∴ A∩B = (0 , 0)

Commented byAina Samuel Temidayo last updated on 19/Sep/20

Exactly, it was stated in the question.

Commented by1549442205PVT last updated on 18/Sep/20

Thank for your detail solution.We can also argue in following way : For n≠0 then (n,2n)≠(2n,3n) For n=0 then (n,2n)=(2n,3n)

Commented byRasheed.Sindhi last updated on 18/Sep/20

Perhaps the source of the question considers: N={1,2,3,...} In that case A∩B=∅

Commented byMJS_new last updated on 19/Sep/20

N had been {1, 2, 3, ...} and N_0 ={0, 1, 2, ...} a few years ago obviously there was a change to N={0, 1, 2, ...} and N^★ ={1, 2, 3, ...} ⇒ confusion