# NP-Complete problem The class of NP-hard problems that are also in NP. The class of NP-C contains the SAT problem as it is in NP and it is NP-hard. if $A,B\in \text{NP-complete}=\text{NP}\cap \text{NP-hard}$ then $A\le B$ and $B\le A$ i.e., $A\sim B$. This means that all problems in NP-C are equivalent and hard, solving one will solve all the other. This is a new type of definition for problem hardness - a problem is hard if solving it allow to solve instantly many other hard problems. ## Created 2023-04-23 13:26