Nested Quantifiers

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October 5th 2008, 07:29 PM
repcvt

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Nested Quantifiers

I was confused with g).

Thx for comming.
October 5th 2008, 11:57 PM
Opalg

$\exists x\,\forall y\, (y\ne x \Rightarrow M(x,y))$ .
October 6th 2008, 12:45 AM
repcvt

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Thank U very much.
But
http://www.mathhelpforum.com/math-he...8b7d28f2-1.gif.

what's different with My anwser :
October 6th 2008, 08:57 AM
Opalg

Quote:

Originally Posted by repcvt

what's different with My anwser :

http://www.mathhelpforum.com/math-he...8b7d28f2-1.gif

The statement $\exists x\,\forall y\, (M(x,y)\wedge y\ne x)$ means that there is a student (x) who has emailed everyone in the class and who is different from everyone in the class. But that would mean in particular that x is different from himself/herself. Obviously that's not possible.

You could have given the alternative solution $\exists x\,\forall y\, ((y= x) \vee M(x,y))$ (meaning that either x=y or x has emailed y).
October 6th 2008, 05:07 PM
repcvt

Quote:

Originally Posted by Opalg

The statement $\exists x\,\forall y\, (M(x,y)\wedge y\ne x)$ means that there is a student (x) who has emailed everyone in the class and who is different from everyone in the class. But that would mean in particular that x is different from himself/herself. Obviously that's not possible.

You could have given the alternative solution $\exists x\,\forall y\, ((y= x) \vee M(x,y))$ (meaning that either x=y or x has emailed y).

Understand it now.Thank U very much.BTW,How did U make that so good express like that

http://www.mathhelpforum.com/math-he...5ac0e526-1.gif

I mean how edit that image like that.look my express,that is so bad.I drawed it handly.:)
October 6th 2008, 11:53 PM
Opalg

Quote:

Originally Posted by repcvt

How did U make that so good express like that

http://www.mathhelpforum.com/math-he...5ac0e526-1.gif

I mean how edit that image like that.

http://www.mathhelpforum.com/math-he...-tutorial.html