Consider the decision problem 2CNFSAT defined as follows:

{ $$\Phi $$ | $$\Phi $$ is a satisfiable propositional formula in CNF with at most two literal per clause}

For example, $$\Phi = \left( {{x_1} \vee {x_2}} \right) \wedge \left( {{x_1} \vee {{\overline x }_3}} \right) \wedge \left( {{x_2} \vee {x_4}} \right)$$ is a Boolean formula and it is in 2CNFSAT.

The decision problem 2CNFSAT is

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?