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)?

The subset-sum problem is defined as follows:
Given a set S of n positive integers and a positive integer W, determine whether there is a subset of S Whose elements sum to W. An algorithm Q solves this problem in O(nW) time. Which of the following statements is false?

Let SHAM₃ be the problem of finding a Hamiltonian cycle in a graph G = (V, E) with |V| divisible by 3 and DHAM₃ be the problem of determining if a Hamiltonian cycle exists in such graphs. Which one of the following is true?

Consider three decision problems P₁, P₂ and P₃. It is known that P₁ is decidable and P₂ is undecidable. Which one of the following is TRUE?