A proof that the set of NP-problems is bigger then the set of P-problems by using a logical consideration

Abstract

Thanks to my short studies about informatics, I present to you this mathematical proof that deals with the sets of P problems, NP-Complete problems and NP-Hard problems in order to prove new formulas about the cardinality of each group of problems and about the intersection of each one of these sets. This work uses logical considerations about the complexity of NP-Hard problems in order to provea theoremabout the complexity ofproblems that allows us to identify NP problems even if their algorithms have infinite time of execution. This work ends by proving that the set of NP-Problems is definitely bigger than the set of P-Problems. Hence, I invite all the readers to develop the results of this article and to present their opinions about the used considerations in this work.