Let R be a relation from N-N defined by R= { (a,b) : a, b belong to N and a= b2 }.Are the following true ?
a) (a,a) ∈R , for all a ∈N
b) (a,b) ∈R implies (b,a) ∈R
c) (a,b) ∈R , (b,c) ∈R implies (a,c) ∈R
Justify your answer in each case.

The correct answer is: statement is wrong.

R is relation from N to N defined by R = { (a, b) : a, b belong to N and a= b² }.
We will consider all the given cases
i) It is not true because a = a²

a²-a = 0

a(a-1) = 0

a = 0 ,1
Hence the given condition is only true for a = 1
Not for all natural numbers.
ii) It is not true because if a = b² , then b = a² is not possible

Eg. 3²  = 9  but 9² > 3
iii) It is not true because
If  then
It means a = b² and b = c² , a = c²
This means a = (c²)² = c⁴

But a = c²
So the given statement is wrong.