Maths-

General

Easy

Question

# 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= b^{2} }.

We will consider all the given cases

i) It is not true because a = a^{2}

a^{2}-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 = b^{2} , then b = a^{2} is not possible

Eg. 3^{2} = 9 but 9^{2} > 3

iii) It is not true because

If then

It means a = b^{2} and b = c^{2} , a = c^{2}

This means a = (c^{2})^{2} = c^{4}

But a = c^{2}

So the given statement is wrong.

^{2}-a = 0

Hence the given condition is only true for a = 1

Not for all natural numbers.

ii) It is not true because if a = b

^{2}, then b = a

^{2}is not possible

^{2}= 9 but 9

^{2}> 3

iii) It is not true because

If then

It means a = b

^{2}and b = c

^{2}, a = c

^{2}

This means a = (c

^{2})

^{2}= c

^{4}

^{2}

So the given statement is wrong.

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