1. Nested Quantifiers

I was confused with g).

Thx for comming.

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

3. Thank U very much.
But
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what's different with My anwser :

4. Originally Posted by repcvt
what's different with My anwser :

The statement $\displaystyle \exists x\,\forall y\, (M(x,y)\wedge y\ne x)$ 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 $\displaystyle \exists x\,\forall y\, ((y= x) \vee M(x,y))$ (meaning that either x=y or x has emailed y).

5. Originally Posted by Opalg
The statement $\displaystyle \exists x\,\forall y\, (M(x,y)\wedge y\ne x)$ 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 $\displaystyle \exists x\,\forall y\, ((y= x) \vee M(x,y))$ (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.

6. 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