Suppose a polynomial time algorithm is discovered that correctly computes the largest clique in a given graph. In this scenario, which one of the following represents the correct Venn diagram of the complexity classes P, NP and NP Complete (NPC)?
Shouldn't the answer be (C) instead? Considering the nature of $\Sigma^*$ and $\emptyset$ which belong to class P but no other problem can be reduced to them.
Clique is in NPC. By definition of NPC, all NP problems can be reduced to Clique in polynomial time. So, if clique can be solved in polynomial time, any NP problem can also be solved in polynomial time making P=NP and hence P=NP=NPC.
Answer is option C.
No problem can be reduced to either $\emptyset $ or $\Sigma^*$.