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.
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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.
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