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

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

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