Question

Question 9 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.

Class X1 - Maths -Relations and Functions Page 46

Answer 1

Given,
R:N------->N defined by
R = {(a,b):a,b∈N and a = b^2}

(i) it's not true . Becoz a = a^2
a(a -1) = 0 , a= 0, 1 hence, it is true only for a = 1 not for other natural number.

(ii) it's not true. I mean statement is false.because if a=b^2, then b=a^2 is not correct statement .
For example,
4 = 2^2 but 4^2 >2

(iii) it's flase. Because
if (a,b)∈R, (b,c)∈R and (a,c)∈R 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 from above.
So, statenent is wrong.