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Not all you know is true This is the biggest piece of a pie and where the familiarity with np complete problems pays. Npc (np complete) is a subset of np, not the other way around

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Completeness always includes being an element of the class the problem is complete for

Is the above definition correct I have a faint notion of what np hard is (that a problem is legit difficult 3 sat for example) I have forgotten what conp hard, and wikipedia tells me that the complement of conp hard is np hard. What if you really do need an exact solution to the problem and the other approaches here won't.

Reduce an arbitrary instance of an np complete problem to an instance of your problem