P-NP Theory

The problem 3-SAT and 2-SAT are

Language L_{1} is polynomial time reducible to language L_{2}. Language L_{3} is polynomial time reducible to L_{2}, which in turn is polynomial time reducible to language L_{4}. Which of the following is/are true?
I. if L_{4} \in P, then L_{2} \in P
II. if L_{1} \in P or L_{3} \in P, then L_{2} \in P
III. L_{1} \in P, if and only if L_{3} \in P
IV. if L_{4} \in P, then L_{1} \in P and L_{3} \in P

Consider two decision problems Q1,Q2 such that Q1 reduces in polynomial time to 3-SAT and 3-SAT reduces in polynomial time to Q2. Then which one of the following is consistent with the above statement?

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 =(x_{1} \vee x_{2}) \wedge (x_{1} \vee \bar{x_{3}}) \wedge (x_{2} \vee x_{4}) 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)?

Which of the following statements are TRUE?
1. The problem of determining whether there exists a cycle in an undirected graph is in P.
2. The problem of determining whether there exists a cycle in an undirected graph is in NP.
3. If a problem A is NP-Complete, there exists a non-deterministic polynomial time algorithm to solve A.

Assuming P \neq NP, which of the following is TRUE?

Let \pi _{A} be a problem that belongs to the class NP. Then which one of the following is TRUE?

For problems X and Y, Y is NP-complete and X reduces to Y in polynomial time. Which of the following is TRUE?

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?