Discrete Math- Irrational numbers, proof or counterexample

[abjf9299]

Homework Statement

Determine if the statement is true or false. Prove those that are true and give a counterexample for those that are false.

If r is any rational number and if s is any irrational number, then r/s is irrational.

Homework Equations

A rational number is equal to the ratio of two other numbers.
An irrational number can't be expressed as the ratio of two other numbers.

The Attempt at a Solution

I said that this statement is false. As my counterexample, I set r = 0 and s = (2)^1/2 .

r/s then equals 0 which is rational.


I have seen several people give different answers to this problem (our professor let's us consult with each other on the homework). Am I right? If I am wrong, could someone give me a proof for this problem?

 

[gb7nash]

If r is any rational number and if s is any irrational number, then r/s is irrational.

You're correct. To prove this is false, you need to provide a counterexample for one situation, which you have done. By different answers though, what do you mean? Do some people think it's true, or are they providing different counterexamples? If they're just providing different counterexamples, there's nothing wrong with that.

 

[abjf9299]

Thanks for the answer! By different answers I mean they think it's true and provided "proofs" to support their assertions, but I know where they made their mistakes now. Thanks again for your help!