Equivalence Relation on R

[Robb]

Homework Statement:

Prove that tilde is an equivalence relation on R

Relevant Equations:

See attached

Can someone please explain what the tilde represents? We have had no info on this to date. I know it has to do with an equivalence relation but not sure what it represents on its own as in part (a) of the attached. Just want to make sure I'm clear. Thanks!

 

[LCKurtz]

Please post the equations here instead of expecting us to download and open some pdf file.

 

[Robb]

 

[LCKurtz]

Read $x \sim y$ as "x is related to y".

 

[WWGD]

To get you started, you need to show (reflexivity) that x~x or x-x is in $\mathbb Q$ Can you take it from here?