**Simplifying Boolean Expressions****Problem 1:**Simplify the following Boolean expression to a minimum number of literals:\[ x'y'z' + x'yz + xy'z + xyz' + xyz \]The aim is to reduce the expression to three literals.**Steps for Simplification:**1. **Identify Common Terms:** - Look for common variables in the terms to factor out and simplify the expression.2. **Apply Boolean Algebra Rules:** - Use rules such as the Consensus Theorem, Distribution, and Absorption laws.3. **Combine Terms:** - Simplify by combining like terms or eliminating redundant terms.The goal is to express the function with the fewest possible variables.

Answered: Simplify the following Boolean…

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

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**Simplifying Boolean Expressions**

**Problem 1:**

Simplify the following Boolean expression to a minimum number of literals:

\[ x'y'z' + x'yz + xy'z + xyz' + xyz \]

The aim is to reduce the expression to three literals.

**Steps for Simplification:**

1. **Identify Common Terms:**
- Look for common variables in the terms to factor out and simplify the expression.

2. **Apply Boolean Algebra Rules:**
- Use rules such as the Consensus Theorem, Distribution, and Absorption laws.

3. **Combine Terms:**
- Simplify by combining like terms or eliminating redundant terms.

The goal is to express the function with the fewest possible variables.

Expert Solution

Step 1: Introducing Boolean Expression

A Boolean expression is a mathematical and logical construct that uses binary variables and logical operations. The variable in a Boolean expression can take only two values: true or false, often represented as 1 or 0 respectively.

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