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**kemposss****Guest**

let me use Ax as "for all" and Ex as "for some" or "there exsists.

now my question is, what is the truth value of:

Ax[(x^2=1) implies (x=-1)] u=R

thanks

**Ricky****Moderator**- Registered: 2005-12-04
- Posts: 3,791

What you wrote reads:

For all x^2 = 1 implies x = -1.

Does the u=R at the end mean that R (the reals) is the universal set? If so, I think you meant:

For all x in R, x^2 = 1 implies x = -1.

Now to make this statement false, all we have to do is find 1 value x in the reals, such that x^2 = 1 and x <> -1. (<> means does not equal).

Can you find it?

"In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..."

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**krassi_holmz****Real Member**- Registered: 2005-12-02
- Posts: 1,905

There might be a mistake. Why didn't you use Ex?

IPBLE: Increasing Performance By Lowering Expectations.

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**Ricky****Moderator**- Registered: 2005-12-04
- Posts: 3,791

I don't think so krassi. It's a good example of how to negate the all quantifier, as well as a good example that shows what breaks down when a function isn't 1-1, if I interpreted it right. Seems to unlikely to just be chance...

"In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..."

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**krassi_holmz****Real Member**- Registered: 2005-12-02
- Posts: 1,905

Oh, yes...

"What's the truth value of..."

*Last edited by krassi_holmz (2006-06-10 02:56:56)*

IPBLE: Increasing Performance By Lowering Expectations.

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