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32) Select the Boolean expression that is equivalent to the function defined in the table blow: x y z f(x, y, z) 0 0 0 1 0 0 10 0 1 0 1 0 1 1 0 1 000 1 0 1 0 1 1 00 1 1 1 1 a. xyz + xyz + xyz b. xyz + xyz + xyz c. xyz + xyz + xyz d. xyz + xyz + xyz

32) Select the Boolean expression that is equivalent to the function defined in the table blow: x y z f(x, y, z) 0 0 0 1 0 0 10 0 1 0 1 0 1 1 0 1 000 1 0 1 0 1 1 00 1 1 1 1 a. xyz + xyz + xyz b. xyz + xyz + xyz c. xyz + xyz + xyz d. xyz + xyz + xyz

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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**Boolean Function Selection** **Question 32**: Select the Boolean expression that is equivalent to the function defined in the table below: **Truth Table** | x | y | z | f(x, y, z) | |---|---|---|-----------| | 0 | 0 | 0 | 1 | | 0 | 0 | 1 | 0 | | 0 | 1 | 0 | 1 | | 0 | 1 | 1 | 0 | | 1 | 0 | 0 | 0 | | 1 | 0 | 1 | 0 | | 1 | 1 | 0 | 0 | | 1 | 1 | 1 | 1 | **Options** a. \( xy\bar{z} + \bar{x}y\bar{z} + xyz \) b. \( x\bar{y}\bar{z} + x\bar{y}z + xyz \) c. \( xyz + x\bar{y}z + xyz \) d. \( \bar{xyz} + \bar{x}y\bar{z} + xyz \)
Transcribed Image Text:**Boolean Function Selection** **Question 32**: Select the Boolean expression that is equivalent to the function defined in the table below: **Truth Table** | x | y | z | f(x, y, z) | |---|---|---|-----------| | 0 | 0 | 0 | 1 | | 0 | 0 | 1 | 0 | | 0 | 1 | 0 | 1 | | 0 | 1 | 1 | 0 | | 1 | 0 | 0 | 0 | | 1 | 0 | 1 | 0 | | 1 | 1 | 0 | 0 | | 1 | 1 | 1 | 1 | **Options** a. \( xy\bar{z} + \bar{x}y\bar{z} + xyz \) b. \( x\bar{y}\bar{z} + x\bar{y}z + xyz \) c. \( xyz + x\bar{y}z + xyz \) d. \( \bar{xyz} + \bar{x}y\bar{z} + xyz \)
### Boolean Expression Selection #### Problem Statement Select the Boolean expression equivalent to the function defined in the table below: #### Truth Table | x | y | z | f(x, y, z) | |---|---|---|----------| | 0 | 0 | 0 | 0 | | 0 | 0 | 1 | 0 | | 0 | 1 | 0 | 1 | | 0 | 1 | 1 | 1 | | 1 | 0 | 0 | 0 | | 1 | 0 | 1 | 1 | | 1 | 1 | 0 | 0 | | 1 | 1 | 1 | 0 | #### Options a. \( \overline{x} y \overline{z} + \overline{x} yz \) b. \( \overline{x} yz + x \overline{y} z + x \overline{y} \overline{z} \) c. \( \overline{x} y \overline{z} + xyz + x \overline{y} z \) d. \( \overline{x} y \overline{z} + x \overline{y} z + x \overline{y} \overline{z} + xyz \) The correct expression matches the rows in the truth table where the output \( f(x, y, z) = 1 \).
Transcribed Image Text:### Boolean Expression Selection #### Problem Statement Select the Boolean expression equivalent to the function defined in the table below: #### Truth Table | x | y | z | f(x, y, z) | |---|---|---|----------| | 0 | 0 | 0 | 0 | | 0 | 0 | 1 | 0 | | 0 | 1 | 0 | 1 | | 0 | 1 | 1 | 1 | | 1 | 0 | 0 | 0 | | 1 | 0 | 1 | 1 | | 1 | 1 | 0 | 0 | | 1 | 1 | 1 | 0 | #### Options a. \( \overline{x} y \overline{z} + \overline{x} yz \) b. \( \overline{x} yz + x \overline{y} z + x \overline{y} \overline{z} \) c. \( \overline{x} y \overline{z} + xyz + x \overline{y} z \) d. \( \overline{x} y \overline{z} + x \overline{y} z + x \overline{y} \overline{z} + xyz \) The correct expression matches the rows in the truth table where the output \( f(x, y, z) = 1 \).
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