3. SAT Problem
The chapter explores the Satisfiability Problem (SAT), defining satisfiable propositions and introducing Conjunctive Normal Form (CNF) as a crucial concept. It discusses methods to determine if a compound proposition is satisfiable and presents a practical application in solving Sudoku puzzles using propositional logic. The chapter emphasizes the complexity of SAT and highlights its relevance in computer science and AI.
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What we have learnt
- A compound proposition is satisfiable if there exists at least one truth assignment that makes it true.
- Conjunctive Normal Form (CNF) is a representation of a compound proposition as a conjunction of clauses, where each clause is a disjunction of literals.
- The SAT problem can be applied to various practical scenarios, including solving Sudoku puzzles, by encoding the problem as a compound proposition.
Key Concepts
- -- Satisfiability Problem (SAT)
- A problem of determining whether a given compound proposition has at least one truth assignment that makes it true.
- -- Conjunctive Normal Form (CNF)
- A way of structuring a logical expression as a conjunction of clauses, where each clause consists of disjunctions of literals.
- -- Clause
- A disjunction of literals within a CNF, representing a part of the overall compound proposition.
- -- Literal
- A variable or the constants true or false, which can be used in clauses.
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