# in detail explaination

• Jul 21st 2009, 11:41 AM
irfan
in detail explaination
Hello for every one,

I have a question about real analysis Q: let S be the cartesian Coordinate plane RxR and define a relation R on S by (a,b)R(c,d) iff a+d=b+c Verify that R is an equivalence relation.

I know that i have to proof R is reflexive, Symmetric and transitive
a) Reflexive: I have to show (a,b)R(a,b) for all (a,b) belong to RxR

b) Symmetric: (a,b)R(c,d) implies (c,d)R(a,b) for all (a,b)R(c,d) belong to RxR

c) Transitive: (a,b)R(c,d) and (c,d)R(e,f) implies that (a,b)R(e.f) for all (a,b),(c,d),(e,f) belong to RxR

can any one explain to me in detail

• Jul 21st 2009, 12:09 PM
Plato
Quote:

Originally Posted by irfan
Hello for every one,

I have a question about real analysis Q: let S be the cartesian Coordinate plane RxR and define a relation R on S by (a,b)R(c,d) iff a+d=b+c Verify that R is an equivalence relation.

b) Symmetric: (a,b)R(c,d) implies (c,d)R(a,b) for all (a,b)R(c,d) belong to RxR

Symmetric: $a + d = b + c\, \Leftrightarrow \,b + c = a + d\, \Leftrightarrow \,c + b = d + a$
• Jul 21st 2009, 12:22 PM
irfan
Thanks
but i nead in detail for whole Q
• Jul 21st 2009, 12:31 PM
Plato
Quote:

Originally Posted by irfan
but i nead in detail for whole Q

It is absolutely not our purpose to do your homework for you.
It is after all your homework. It is designed to teach you.
So you do something for yourself. We can help if you will do something.

On the other hand, if you are completely lost then we are not responsible for that.
In that case you need to talk with those giving the course instruction.