1. The problem statement, all variables and given/known data 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. 2. Relevant 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. 3. 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 lets us consult with each other on the homework). Am I right? If I am wrong, could someone give me a proof for this problem?