Let R be a relation from to N defined by R = {(a, b); a, b ∈ & N, and a = b²}. Are the following true.
(i) (a, b) ∈ R, for all a ∈ & N
(ii) (a, b) ∈ R ⇒ (b, a) ∈ R.
(iii) (a, b) ∈ R, (b, c) ∈ R ⇒ (a, c) ∈ R.

Question

Let R be a relation from to N defined by R = {(a, b); a, b ∈ & N, and a = b²}. Are the following true.
(i) (a, b) ∈ R, for all a ∈ & N
(ii) (a, b) ∈ R ⇒ (b, a) ∈ R.
(iii) (a, b) ∈ R, (b, c) ∈ R ⇒ (a, c) ∈ R.

Shiksha Nation · Accepted Answer

(i) a = a2, is true only when a = 0 ∉ &Naturals; hence it is not a relation.(ii) a = b2, and b = a2 is not true for all a,b ∈ & N, hence it is not a relation.(iii) a = b2, b = c2∴ a = (c2)2 = c4 ⇒ a ≠ c2. It is not a relation.

Let R be a relation from to N defined by R = {(a, b); a, b ∈ & N, and a = b2}. Are the following true.(i) (a, b) ∈ R, for all a ∈ & N(ii) (a, b) ∈ R ⇒ (b, a) ∈ R.(iii) (a, b) ∈ R, (b, c) ∈ R ⇒ (a, c) ∈ R.

Verified Answer

Let R be a relation from to N defined by R = {(a, b); a, b ∈ & N, and a = b²}. Are the following true.
(i) (a, b) ∈ R, for all a ∈ & N
(ii) (a, b) ∈ R ⇒ (b, a) ∈ R.
(iii) (a, b) ∈ R, (b, c) ∈ R ⇒ (a, c) ∈ R.