Math Help - in detail explaination

1. 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

thanks in advance

2. 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: $a + d = b + c\, \Leftrightarrow \,b + c = a + d\, \Leftrightarrow \,c + b = d + a$

3. Thanks

but i nead in detail for whole Q

4. 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.