How can this be broken up into a math statement?

Question

I'm trying to solve this question: "Prove or disprove that the product of two irrational numbers is irrational" but I am having trouble breaking this question up into a math statement.

Is an appropriate statement "If a and b are irrational, then ab is irrational"?

Sure. Again, though, they are asking you to prove that (if it is true) or to disprove it (if it is false). Hint: if it is false, a single counterexample is all you need to disprove it. — lulu, Sep 19 '16 at 02:18

score 1 · Accepted Answer · answered Sep 19 '16 at 02:19

1

Yes, that is a correct formulation of the statement you need to prove or disprove.

What do you think? Is the statement true or false?

answered Sep 19 '16 at 02:19

Anon

5,489

2

I think it is false. One counterexample is a = b = $\sqrt{2}$. Then $ab = 2$ which is rational. – Jason Sep 19 '16 at 02:25
And that's a valid disproof. – Anon Sep 19 '16 at 02:50

score 1 · Answer 2 · answered Sep 19 '16 at 02:25

1

Yes, that is an appropriate statement. In fact, that is a good proposition with which to begin a proof by way of reductio ad absurdum.

answered Sep 19 '16 at 02:25

Michael

11

How can this be broken up into a math statement?

2 Answers2