Well I have to prove the following statements are equivalent:(adsbygoogle = window.adsbygoogle || []).push({});

a. y is a rational number

b. y/3 is a rational number

c. 2y+5 is a rational number

So a -> b -> c -> a

I'm not quite sure how you are suppose to prove something is rational however.

I started like this:

* y = q/r Where q & r are integers, r is not 0, no common factors other than 1 [Therefore rational]

* y/3

q/r/3 ... (q/r)(1/3)= q/3r ... Which is rational because everything is integer math?

* 2y+5 ... 2(q/r) + (5/1) ... same reason

This doesn't seem to work like the ones I've done before with proving something is even (2n) or odd (2n+1). Is there some step I'm not getting?

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# Homework Help: Proving equivalence

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