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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?