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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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Question
![**Simplifying Logic Expressions Using Boolean Properties**
In this exercise, you will simplify a logical expression step by step. Use the pull-down menus to select the correct Boolean property for each transformation.
1. **Expression:** \( z \lor \neg(y \land z) \)
2. **Step 1:** \( z \lor \neg y \lor \neg z \)
- [Select the Boolean property]
3. **Step 2:** \( z \lor \neg z \lor \neg y \)
- [Select the Boolean property]
4. **Step 3:** \( 1 \lor \neg y \)
- [Select the Boolean property]
5. **Step 4:** \( 1 \)
- [Select the Boolean property]
Use reasoning and understanding of Boolean laws such as De Morgan's Theorems and the properties of OR to determine each step accurately.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F508cad95-79c4-422c-a0c1-ca05982216ff%2F33b7839a-243a-476f-9d4f-a31056267baa%2Fnknkc64_processed.png&w=3840&q=75)
Transcribed Image Text:**Simplifying Logic Expressions Using Boolean Properties**
In this exercise, you will simplify a logical expression step by step. Use the pull-down menus to select the correct Boolean property for each transformation.
1. **Expression:** \( z \lor \neg(y \land z) \)
2. **Step 1:** \( z \lor \neg y \lor \neg z \)
- [Select the Boolean property]
3. **Step 2:** \( z \lor \neg z \lor \neg y \)
- [Select the Boolean property]
4. **Step 3:** \( 1 \lor \neg y \)
- [Select the Boolean property]
5. **Step 4:** \( 1 \)
- [Select the Boolean property]
Use reasoning and understanding of Boolean laws such as De Morgan's Theorems and the properties of OR to determine each step accurately.
Expert Solution
Step 1
De Morgan's Theorem/Law
The following are De Morgan’s theorems/laws:
1. ( A + B )’ = A’ . B’
Truth Table:
| A | B | A + B | (A + B)' | A' | B' | A' . B' |
| 0 | 0 | 0 | 1 | 1 | 1 | 1 |
| 0 | 1 | 1 | 0 | 1 | 0 | 0 |
| 1 | 0 | 1 | 0 | 0 | 1 | 0 |
| 1 | 1 | 1 | 0 | 0 | 0 | 0 |
2. ( A . B )' = A' + B'
Truth Table:
| A | B | A . B | (A . B)' | A' | B' | A' + B' |
| 0 | 0 | 0 | 1 | 1 | 1 | 1 |
| 0 | 1 | 0 | 1 | 1 | 0 | 1 |
| 1 | 0 | 0 | 1 | 0 | 1 | 1 |
| 1 | 1 | 1 | 0 | 0 | 0 | 0 |
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