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1. Truth Table Construct a truth table for the following: a) F(X,Y,Z) = y₁z+xz + x 0 0 0 0 1 1 1 1 y Z 0 0 0 1 0 1 1 1 0 0 0 1 1 0 1 1 LL F b) F(x, y, z) = x'x'Z + X'V X y 0 0 00 0 0 1 N 0 1 1 0 1 1 0 0 1 0 1 1 1 0 1 1 1 LL F

1. Truth Table Construct a truth table for the following: a) F(X,Y,Z) = y₁z+xz + x 0 0 0 0 1 1 1 1 y Z 0 0 0 1 0 1 1 1 0 0 0 1 1 0 1 1 LL F b) F(x, y, z) = x'x'Z + X'V X y 0 0 00 0 0 1 N 0 1 1 0 1 1 0 0 1 0 1 1 1 0 1 1 1 LL F

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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## Class Exercises #9 ### 1. Truth Table Construct a truth table for the following: **a) F(x, y, z) = y'z + xz** | x | y | z | F | |---|---|---|---| | 0 | 0 | 0 | 0 | | 0 | 0 | 1 | 1 | | 0 | 1 | 0 | 0 | | 0 | 1 | 1 | 0 | | 1 | 0 | 0 | 0 | | 1 | 0 | 1 | 1 | | 1 | 1 | 0 | 0 | | 1 | 1 | 1 | 1 | **b) F(x, y, z) = x'y'z + x'y** | x | y | z | F | |---|---|---|---| | 0 | 0 | 0 | 0 | | 0 | 0 | 1 | 0 | | 0 | 1 | 0 | 1 | | 0 | 1 | 1 | 1 | | 1 | 0 | 0 | 0 | | 1 | 0 | 1 | 0 | | 1 | 1 | 0 | 1 | | 1 | 1 | 1 | 1 | ### Explanation **Truth Table for F(x, y, z) = y'z + xz** - This truth table lists all possible combinations of the binary inputs (x, y, z) and their corresponding output (F). - The function `y'z + xz` uses logical AND and OR operations, where `y'` is the logical NOT of y. **Truth Table for F(x, y, z) = x'y'z + x'y** - Similar to the first truth table, this lists all possible combinations of binary inputs (x, y, z) and their corresponding output (F). - The function `x'y'z + x'y` uses logical AND and OR operations, where `x'` and `y'` are the logical NOT of x and y respectively.
Transcribed Image Text:## Class Exercises #9 ### 1. Truth Table Construct a truth table for the following: **a) F(x, y, z) = y'z + xz** | x | y | z | F | |---|---|---|---| | 0 | 0 | 0 | 0 | | 0 | 0 | 1 | 1 | | 0 | 1 | 0 | 0 | | 0 | 1 | 1 | 0 | | 1 | 0 | 0 | 0 | | 1 | 0 | 1 | 1 | | 1 | 1 | 0 | 0 | | 1 | 1 | 1 | 1 | **b) F(x, y, z) = x'y'z + x'y** | x | y | z | F | |---|---|---|---| | 0 | 0 | 0 | 0 | | 0 | 0 | 1 | 0 | | 0 | 1 | 0 | 1 | | 0 | 1 | 1 | 1 | | 1 | 0 | 0 | 0 | | 1 | 0 | 1 | 0 | | 1 | 1 | 0 | 1 | | 1 | 1 | 1 | 1 | ### Explanation **Truth Table for F(x, y, z) = y'z + xz** - This truth table lists all possible combinations of the binary inputs (x, y, z) and their corresponding output (F). - The function `y'z + xz` uses logical AND and OR operations, where `y'` is the logical NOT of y. **Truth Table for F(x, y, z) = x'y'z + x'y** - Similar to the first truth table, this lists all possible combinations of binary inputs (x, y, z) and their corresponding output (F). - The function `x'y'z + x'y` uses logical AND and OR operations, where `x'` and `y'` are the logical NOT of x and y respectively.
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