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What is the definition of P, NP, NP-complete and NP-hard?

here is a good answer but it really doesn't answer mym question.

np-hard-: a problem A is NP hard if for all B$\in$NP, B is polynomial time reducible to A.(i.e A is easier than B). Then why is A called NP Hard? It should be called NP easy problem? Isn't it?

np complete-: A problem is NP complete if problem is in both NP and NP hard.

SO basically np complete=np hard. What is the difference between np hard and np complete?

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So I got it. NP hard problem is not necessarily in NP. That's the difference.

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