In Boolean logic, a sentence is in 3-Conjunctive Normal Form (abbreviated 3-CNF) if it of the formC1 ^ C2 ^ C3 ^ .…. A Cm, where S is the conjunction of m clauses, with each clause being a disjunction ofSthree literals.We say that S is satisfiable if there exists an assignment of TRUE/FALSE values to each variable so that the entiresentence S evaluates to TRUE.For example, in the last class, we showed that the following 3-CNF sentence, with m=8 clauses, is not satisfiable.D) ^ (B v č v D) ^ (c vĀ v D) ^ (A(A v(Bv č v D) A (c v Ā v D) a (A v B V C) ^ (a v B v C)A Vv B v D)S =AVВVA V BLet 3-SAT be the decision problem that inputs a 3-CNF sentence S, and outputs YES if S is satisfiable, and outputs NOif S is not satisfiable.Consider these four statements.A. 3-SAT is in P, but is almost surely not in NPB. 3-SAT is in NP, but is almost surely not in PC. 3-SAT is in P and is also in NPD. 3-SAT is neither in P nor in NPDetermine which of these four statements is correct. Answer A, B, C, or D.

Here we will check 3CNF-SAT firstly learn what is CNF- If we put a bunch of disjunctive clauses…

Answered: In Boolean logic, a sentence is S = C¡…

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In Boolean logic, a sentence is S = C¡ ^ C2 ^ C3 ^ …· ^ three literals.

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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Question

In Boolean logic, a sentence is in 3-Conjunctive Normal Form (abbreviated 3-CNF) if it of the form
C1 ^ C2 ^ C3 ^ .…. A Cm, where S is the conjunction of m clauses, with each clause being a disjunction of
S
three literals.
We say that S is satisfiable if there exists an assignment of TRUE/FALSE values to each variable so that the entire
sentence S evaluates to TRUE.
For example, in the last class, we showed that the following 3-CNF sentence, with m=8 clauses, is not satisfiable.
D) ^ (B v č v D) ^ (c vĀ v D) ^ (A
(A v
(Bv č v D) A (c v Ā v D) a (A v B V C) ^ (a v B v C)
A V
v B v D)
S =
AVВV
A V B
Let 3-SAT be the decision problem that inputs a 3-CNF sentence S, and outputs YES if S is satisfiable, and outputs NO
if S is not satisfiable.
Consider these four statements.
A. 3-SAT is in P, but is almost surely not in NP
B. 3-SAT is in NP, but is almost surely not in P
C. 3-SAT is in P and is also in NP
D. 3-SAT is neither in P nor in NP
Determine which of these four statements is correct. Answer A, B, C, or D.

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