# Math Proof

1. Jun 15, 2015

### wfc

How could you prove that if x*y ≠ -1, then x/y ≠ -1?

x*y ≠ -1 → x ≠ -1/y

I'm not sure where to go after that.

2. Jun 15, 2015

### wabbit

You don't prove it, because it isn't true. Can you find a couterexample ?

3. Jun 15, 2015

### micromass

Staff Emeritus
Assuming it were true (which it isn't), the best way would be to do contraposition. It would then suffices to show that $x/y = -1$ implies $xy = -1$.

4. Jun 15, 2015

### wfc

Can you explain why it isn't true? I'm still confused.

And where you say x/y = -1, then xy = -1, I can't come up with an example where that would work?

5. Jun 15, 2015

### micromass

Staff Emeritus
If you can't come up with an example where that would work, then that means it's false.

6. Jun 15, 2015

### wabbit

What you need to find is an example of $x,y$ such that $x/y=-1$ and $xy\neq -1$ .

Once you've done that you've proved that your initial statement $(xy\neq -1\Rightarrow x/y\neq -1 )$ is false

7. Jun 16, 2015

### FL0R1

if x ≠ -1/y then (-1/y)/y ≠ -1 -> here we go that -1 ≠ -1 so its not true

8. Jun 16, 2015

### wabbit

No, this does not follow at all.

Last edited: Jun 16, 2015
9. Jun 16, 2015

### Svein

Counterexample:

Put x = -2, y=2. Then x⋅y = -4 (which is not -1) and x/y = -1.

10. Jun 16, 2015

### wabbit

You don't leave any stone unturned :)

11. Jun 17, 2015

### Svein

I am a mathematician. I have to turn them.

12. Jun 21, 2015