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

1.	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.
Answer» 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 ∈ 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.

Answer»

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.