I am a bit confused in this logic according to me all NPC are NP so that means all NPC are reducible to NP but since NPC are NP-hard as well so I guess that is not possible since if x is reduced to y that means y must be harder than or equal to x that means x cant be NPC since NP-hard is not easier than NP , so is it that all NP are reducible to NPC or all NPC are reducible to NP , I am a bit confused in this , so please help.