Nested Quantifiers

**repcvt** · October 5th 2008, 07:29 PM

I was confused with g).

Thx for comming.

**Opalg** · October 5th 2008, 11:57 PM

$\exists x\,\forall y\, (y\ne x \Rightarrow M(x,y))$ .

**repcvt** · October 6th 2008, 12:45 AM

Thank U very much.
But

.

what's different with My anwser :

**Opalg** · October 6th 2008, 08:57 AM

Originally Posted by repcvt

what's different with My anwser :

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).

**repcvt** · October 6th 2008, 05:07 PM

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

I mean how edit that image like that.look my express,that is so bad.I drawed it handly.

**Opalg** · October 6th 2008, 11:53 PM

Originally Posted by repcvt

How did U make that so good express like that

I mean how edit that image like that.

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

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