3. Consider two Boolean functions, f(x,y,z) and g(x,y,z). Use truth tables to prove the two functions, f(x,y,z) and g(x,y,z) are logically equivalent or not. f(x,y,z)=x(y'z + y) + x'(y + z')' g(x,y,z) = yz' + xy
3. Consider two Boolean functions, f(x,y,z) and g(x,y,z). Use truth tables to prove the two functions, f(x,y,z) and g(x,y,z) are logically equivalent or not. f(x,y,z)=x(y'z + y) + x'(y + z')' g(x,y,z) = yz' + xy
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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![**Consider two Boolean functions,** \( f(x, y, z) \) **and** \( g(x, y, z) \). **Use truth tables to prove the two functions,** \( f(x, y, z) \) **and** \( g(x, y, z) \) **are logically equivalent or not.**
\[ f(x, y, z) = x(y'z + y) + x'(y + z')' \]
\[ g(x, y, z) = yz' + xy \]
**Instructions:**
- Construct truth tables for both functions.
- Evaluate the outputs for all combinations of inputs \( x, y, \) and \( z \).
- Compare the outputs to determine if the functions are equivalent.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F63a2ecd4-d40e-4f58-bfeb-302941b5ae7f%2F5a41f13e-5867-4c2b-8cd2-a9052d1c2a51%2F5k6ke9_processed.png&w=3840&q=75)
Transcribed Image Text:**Consider two Boolean functions,** \( f(x, y, z) \) **and** \( g(x, y, z) \). **Use truth tables to prove the two functions,** \( f(x, y, z) \) **and** \( g(x, y, z) \) **are logically equivalent or not.**
\[ f(x, y, z) = x(y'z + y) + x'(y + z')' \]
\[ g(x, y, z) = yz' + xy \]
**Instructions:**
- Construct truth tables for both functions.
- Evaluate the outputs for all combinations of inputs \( x, y, \) and \( z \).
- Compare the outputs to determine if the functions are equivalent.
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