Question

Let A={1,2,3....9}and R be the relation in A×A defined by (a,b)R(c,d) if a+d=b+c for (a,b),(c,d) in A×A.Prove that R is an equivalence relation and also obtain the equivalent class[(2,5)]

Answer 1

Hey mate,.

A={1,2,3,4,5,6,7,8,9}

From a and b,

2+b=5+a

(2,5)R(1,4)=>2+4=5+1

[{2,5}]=[(1,4)(2,5)(3,6)(4,7)(5,8)(6,9)}]

It's the equality class under relation R.

Hope it will help you

✌️Sai

Answer 2

A={1,2,3......9}

from a and b

2+b=5+a

(2,5)R (1,4)=>2+4=5+1

[{2,5}]=[{(1,4)(2,5)(3,6)(4,7)(5,8)}]

it is equality class under relation R