Answered: Describe the process of converting a…

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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Transcribed Image Text:**Question: Describe the process of converting a logical formula into DNF. What are the steps involved?** When addressing the topic of converting a logical formula into Disjunctive Normal Form (DNF), it's essential to break the process down into clear, manageable steps. DNF is a standardized way to express logical formulas where the formula is a disjunction (OR) of conjunctions (AND) of literals. Here is a detailed explanation of the steps involved: 1. **Expand all negations**: Ensure all NOT operators (¬) apply directly to individual variables by using De Morgan's laws. For instance, the expression ¬(A ∧ B) becomes ¬A ∨ ¬B, and ¬(A ∨ B) becomes ¬A ∧ ¬B. 2. **Distribute ANDs over ORs**: Apply the distributive laws to move conjunctions inside disjunctions where possible. For example, the expression A ∧ (B ∨ C) should be rewritten as (A ∧ B) ∨ (A ∧ C). 3. **Flatten nested expressions**: Simplify any nested logical operations to ensure the expression is represented in a structure where conjunctions are nested inside disjunctions. For instance, ((A ∧ B) ∨ C) is already in a DNF structurally. 4. **Combine and simplify terms**: Eliminate any duplicate terms and simplify the expression if possible. For example, A ∨ A reduces to A. By following these steps, one can systematically convert a complex logical formula into Disjunctive Normal Form, making it easier to analyze and use in various applications, such as digital logic design and Boolean algebra simplifications.

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