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Which of the following equations correctly reflects the truth table shown below?

Which of the following equations correctly reflects the truth table shown below?

Database System Concepts
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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The image presents a logic problem asking which of the given equations match the truth table provided. Here's a detailed breakdown: ### Truth Table: | x | y | z | F | |---|---|---|---| | 0 | 0 | 0 | 0 | | 0 | 0 | 1 | 0 | | 0 | 1 | 0 | 1 | | 0 | 1 | 1 | 1 | | 1 | 0 | 0 | 1 | | 1 | 0 | 1 | 1 | | 1 | 1 | 0 | 1 | | 1 | 1 | 1 | 1 | ### Equations: 1. \( x'y'z + xy'z + xy'z' + xyz' + xyz \) 2. \( (xy'z + x'yz' + x'yz + x'yz' + x'yz)' \) 3. \( xy'z + x'yz' + x'yz + x'yz' + x'yz \) 4. \( (x'yz' + x'yz + xy'z' + xyz' + xyz)' \) ### Explanation: - **Truth Table**: The table consists of four columns representing variables \( x \), \( y \), \( z \), and the function \( F \). The function output \( F \) is true (1) for all combinations of inputs except the first two where both \( y \) and \( z \) are 0. - **Equations**: The task is to determine which equation matches the true outputs (1s) listed in the truth table. Each option provides a different Boolean expression that can be tested against the truth table to identify the correct match.
Transcribed Image Text:The image presents a logic problem asking which of the given equations match the truth table provided. Here's a detailed breakdown: ### Truth Table: | x | y | z | F | |---|---|---|---| | 0 | 0 | 0 | 0 | | 0 | 0 | 1 | 0 | | 0 | 1 | 0 | 1 | | 0 | 1 | 1 | 1 | | 1 | 0 | 0 | 1 | | 1 | 0 | 1 | 1 | | 1 | 1 | 0 | 1 | | 1 | 1 | 1 | 1 | ### Equations: 1. \( x'y'z + xy'z + xy'z' + xyz' + xyz \) 2. \( (xy'z + x'yz' + x'yz + x'yz' + x'yz)' \) 3. \( xy'z + x'yz' + x'yz + x'yz' + x'yz \) 4. \( (x'yz' + x'yz + xy'z' + xyz' + xyz)' \) ### Explanation: - **Truth Table**: The table consists of four columns representing variables \( x \), \( y \), \( z \), and the function \( F \). The function output \( F \) is true (1) for all combinations of inputs except the first two where both \( y \) and \( z \) are 0. - **Equations**: The task is to determine which equation matches the true outputs (1s) listed in the truth table. Each option provides a different Boolean expression that can be tested against the truth table to identify the correct match.
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