Hi

I want to negate the following statements. Please check if I am doing it correctly.

1)There exists p > 0 such that for every x we have f(x+p)= f(x)

2) For all there exists such that

whenever x and t are in D and satisfy

, then

3)For all there exists such that

whenever and ,

then

Following are my negated statements

1)For all there exists x such that

2)There exists such that for every

there exists x and t in D such that and

3)There exists such that for every

there exists such that

and

Please tell me if I am doing it right. I have followed the examples given in my book.

The book is "A Friendly Introduction to Analysis: Single and Multivariable, second edition" Author- Witold Kosmala

I am not satisfied with his treatment of the topic there. He discusses these things under the topic of "Proof Techniques", where he also talk talks about methods of proofs, like contradiction , contrapositive.

If you can suggest a good source on internet ( preferably free) where they discuss

negation of the mathematical statements, please suggest me.

thanks

newton