Abrastract Algebra: Show that ~ is an equivalence relation.

I need help in this one:

Let m, n, and s be positive integers. Suppose m/n ~ r/s if and only if ms = nr. Show that ~ is an equivalence relation.

Kidia, will you tell us what is the purpose of this list of questions has? Are you studying for some sort of exit exam from a mathematics program of study?

This current question is absolutely trivial if one knows anything about equivalence relations! Thus, if you are studying for such an exam you may be in trouble. But if not for an exam, then what explains this odd list of problems?

pka said:

Kidia, will you tell us what is the purpose of this list of questions has? Are you studying for some sort of exit exam from a mathematics program of study?

This current question is absolutely trivial if one knows anything about equivalence relations! Thus, if you are studying for such an exam you may be in trouble. But if not for an exam, then what explains this odd list of problems?

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My friend I am just a learner and not studing for the exams but for understanding the concept and I works with problems when get stack I transfer it to FreeMathsHelp for your help,so I request you don feel boared with my problems.Thanks.

It's not a matter of "feeling bored". It's a matter, as the tutor made fairly clear, of feeling confused. These questions show little or no cohesion with respect to subject, and some of them are so simple that one wonders why you cannot get started.

If you are saying that you are doing self-study, then it might be wise to consider hiring a tutor who can help guide you through your eclectic studies. It would appear that you are missing a lot of material, and a tutor, by working face to face with you and your books and by reviewing the material and re-teaching anything you've missed, can help minimize these gaps. This gap-filling, re-teaching process is a service that, unfortunately, we simply cannot provide.

I apologize for any confusion, and wish you well in your studies.

Eliz.