If K is bounded, then K is compact
solution: if K is Not bounded, then K 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".
Apparently, the poblem is to construct the negation, not a corollary. OP: Please post the complete problem in the body of the message.
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'"?