# Thread: Negation ... need to know if correct

1. ## Negation ... need to know if correct

If K is bounded, then K is compact

solution: if K is Not bounded, then K is not compact

2. ## Re: Negation ... need to know if correct

Sorry its suppose to read "If K is closed and bounded, then K is Compact"

3. ## Re: Negation ... need to know if correct

Originally Posted by Odail
If K is bounded, then K is compact

solution: if K is Not bounded, then K is not compact
This is not the negation of the first statement.

What would you do if you wanted to find a countereample to the first statement? Which properties should K possess to be a counterexample?

4. ## Re: Negation ... need to know if correct

try to find and instance or example that shows even though K is bounded it is not Compact

5. ## Re: Negation ... need to know if correct

Originally Posted by Odail
If K is bounded, then K is compact

solution: if K is Not bounded, then K is not compact
If K is a man, then K is human.

Would you then think it reasonable to conclude that

If K is not a man, then K is not human.

6. ## Re: Negation ... need to know if correct

No .... if K is not a human, then K is not a man

7. ## Re: Negation ... need to know if correct

Originally Posted by Odail
try to find and instance or example that shows even though K is bounded it is not Compact
Pretty much. One remark is that the negation of a statement is also a statement and not a command ("Try to find..."). Using your correction "If K is closed and bounded", the negation of the original statement would be, "K is closed and bounded but not compact".

Originally Posted by JeffM
If K is a man, then K is human.

Would you then think it reasonable to conclude that

If K is not a man, then K is not human.
Apparently, the poblem is to construct the negation, not a corollary. OP: Please post the complete problem in the body of the message.

8. ## Re: Negation ... need to know if correct

Odail

I have looked at several of your posts. They seem to be all over the place. We might be better able to help you if we had some clue about where these questions are coming from. Moreover, it is important to give a complete and exact statement of the problem. Is this question simply "What is the negation of 'If K is closed and bounded, then K is compact'"?

9. ## Re: Negation ... need to know if correct

Yes your construction of the statement is correct i made a mistake the first time i posted it ...

10. ## Re: Negation ... need to know if correct

The questions are basically tutorials questions that i don't have the answer to that im using to study for an exam

11. ## Re: Negation ... need to know if correct

Originally Posted by Odail
The questions are basically tutorials questions that i don't have the answer to that im using to study for an exam
@Odail, here is the rule:
The negation of "If P then Q" is " P and not Q".

$\neg \left( {P \to Q} \right) \equiv \neg \left( {\neg P \vee Q} \right) \equiv \left( {P \wedge \neg Q} \right)$