Another Relations question

[Riothouse21]

Here is another one:

Define a relation R on R x R by (x,y)R(w,z) if x-y =w-z.
Prove that R isan equivalence relation.



Also, Describe [(5,3)] the Equivalence Class containing (5,3).

 

[pka]

Define a relation R on R x R by (x,y)R(w,z) if x-y =w-z.
Prove that R isan equivalence relation.
Also, Describe [(5,3)] the Equivalence Class containing (5,3).

You need to show some effort on this one.


Why is it true that \(\displaystyle (5,3)\mathcal{R}(6,4)~?\)

 

[Riothouse21]

I know I need to show that for it to be an equivalence relation: must be reflexive, symmetric, and transitive. So I need to show that there is a value of x-y that is in w-z and that there is a value of w-z that is in x-y (Reflexive). For symmetric, a value in x-y that is in w-z and a value in z-w that is in y-x. Transitive, need to show that a=b , b=c so a=c. It is showing the written proof that is my weakness.

 

[stapel]

I know I need to show that for it to be an equivalence relation: must be reflexive, symmetric, and transitive. So I need to show that there is a value of x-y that is in w-z and that there is a value of w-z that is in x-y (Reflexive). For symmetric, a value in x-y that is in w-z and a value in z-w that is in y-x. Transitive, need to show that a=b , b=c so a=c. It is showing the written proof that is my weakness.

Pick generic elements. See if they comply with the rules. Do this just like they showed in the worked examples in your book and in your class notes.