Let R be a relation from N to N defined by R={(a,b):a,b ϵ N and a=b2}

1.	Let R be a relation from N to N defined by R={(a,b):a,b ϵ N and a=b2}. 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.
Answer» 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 ϵ N and a=b2}. 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.

Answer»

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.