Let R be a relation from N to N defined by R - a - b - a - b - N- and -a - b 2-Are the following statements true -i a - a - R for all a - Nii a - b - R - b - a - R-iii a - b - R and b - c - R - a - c - R-

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Definition of Relations

Let R be a re...

Question

Let R be a relation from N to N defined by R = {(a, b) : $a, b ϵ N$ and $a = b^{2}$ }.

Are the following statements true ?

(i) $(a, a) ϵ R$ for all $a ϵ N$

(ii) $(a, b) ϵ R \Rightarrow (b, a) ϵ R .$

(iii) $(a, b) ϵ R$ and $(b, c) ϵ R \Rightarrow (a, c) ϵ R .$

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Let R be a relation from N to N defined by R = {(a, b): a, b ∈ N and a = b²}. Are the following true?

(i) (a, a) ∈ R, for all a ∈ N

(ii) (a, b) ∈ R, implies (b, a) ∈ R

(iii) (a, b) ∈ R, (b, c) ∈ R implies (a, c) ∈ R.

Justify your answer in each case.

Let R be a relation from N to N defined by $R = {(a, b) : a, b ϵ N$ and $a = b^{2}$ }. Are the following true?

(i) $(a, a) ϵ R$ for all $a ϵ N$

(ii) $(a, a) ϵ R$ implies $(b, a) ϵ R$

(iii) $(a, b) ϵ R, (b, c) ϵ R$ implies $(a, c) ϵ R$

Justify your answer in each case.

Let R be a relation from N to N defined by R = {(a, b): a, b $\in$ N and a = $b^{2}$ }. Which of the following is/are true?

(i) (a, a) $\in$ R, for all a $\in$ N

(ii) (a, b) $\in$ R, implies (b, a) $\in$ R

(iii) (a, b) $\in$ R, (b, c) $\in$ R implies (a, c) $\in$ R

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