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## #1 2006-06-06 18:39:23

kemposss
Guest

### logic

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

## #2 2006-06-07 01:25:01

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

### Re: logic

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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## #3 2006-06-09 02:42:20

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

### Re: logic

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

IPBLE:  Increasing Performance By Lowering Expectations.

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## #4 2006-06-09 09:18:43

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

### Re: logic

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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## #5 2006-06-10 02:56:32

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

### Re: logic

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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