NP Problem and reduction I've read that "Every problem in NP can be reduced to every NP-complete problem".
I want to know why the term "Every" is important.If we have one problem in NP that is reduced to one NP complete problem then what will be the problem.
Since NP-Complete problems can be reduced to each other, If we can reduce a problem to a specific NP-Complete problem. It means that we can reduce it to any NP-Complete problem.
The reason is All problems in NP-Complete can be reduced to SAT and SAT to 3-SAT and 3-SAT to CLIQUE and so forth. So reducing to a problem in NP-Complete means reducing to all problems in NP-Complete.