Define the following predicates:• A(x) : x is on the board of directors."• E(x) : x earns more than $100, 000.• W(x) : x works more than 60 hours per week.The domain is the set of all employees of a certain company. Match each English statement with its equivalent logical expression.? v 1. Everyone who works more than 60 hours per week earns more than $100,000.A. 3x(E(x) ^ ¬W(x))B. Vx(W(x) → E(x))C. Ex(¬A(x) → E(x))D. Vx(W(x) ^ E(x))E. 3x(¬A(x) ^ E(x))F. 3x(A(x) ^ ¬E(x)^ W(x))G. Ex(A(x) V ¬E(x) V W(x))H. Vx(A(x) → E(x))I. Vx(A(x) ^ E(x))2 v 2. Someone on the board of directors does not earn more that $100.000 and works more than 60 hours per week.? v 3. Every member of the board of directors earns more than $100,000.2. v 4. There is someone who is not on the board of directors and earns more than $100,000.? v 5. There is someone who earns more than $100,000, but does not work more than 60 hours per week.

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Define the following predicates: • A(x) : x is on the board of directors." E(x) : x earns more than $100, 000. • W(x) : x works more than 60 hours per week. The domain is the set of all employees of a certain company. Match each English statement with its equivalent logical expression. ? 1. Everyone who works more than 60 hours per week earns more than $100,000. A. Ex(E(x) ^ ¬W(x)) B. Vx(W(x) → E(x)) C. Ex(¬A(x) → E(x)) D. Vx(W(x) ^ E(x)) E. 3x(¬A(x) ^ E(x)) F. 3x(A(x) A ¬E(x)^ W(x)) G. 3x(A(x) V ¬E(x) V W(x)) H. Vx(A(x) → E(x)) I. Vx(A(x) A E(x)) 2. Someone on the board of directors does not earn more that $100,000 and works more than 60 hours per week. ? v 3. Every member of the board of directors earns more than $100,000. 2. v 4. There is someone who is not on the board of directors and earns more than $100,000. 5. There is someone who earns more than $100,000, but does not work more than 60 hours per week.

Define the following predicates: • A(x) : x is on the board of directors." E(x) : x earns more than $100, 000. • W(x) : x works more than 60 hours per week. The domain is the set of all employees of a certain company. Match each English statement with its equivalent logical expression. ? 1. Everyone who works more than 60 hours per week earns more than $100,000. A. Ex(E(x) ^ ¬W(x)) B. Vx(W(x) → E(x)) C. Ex(¬A(x) → E(x)) D. Vx(W(x) ^ E(x)) E. 3x(¬A(x) ^ E(x)) F. 3x(A(x) A ¬E(x)^ W(x)) G. 3x(A(x) V ¬E(x) V W(x)) H. Vx(A(x) → E(x)) I. Vx(A(x) A E(x)) 2. Someone on the board of directors does not earn more that $100,000 and works more than 60 hours per week. ? v 3. Every member of the board of directors earns more than $100,000. 2. v 4. There is someone who is not on the board of directors and earns more than $100,000. 5. There is someone who earns more than $100,000, but does not work more than 60 hours per week.

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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Concept explainers

Predicates

A predicate is a function defined with set of variables, which returns the result True or False. The output of a predicate is a Boolean value as a response when given a set of parameters:

Question

Define the following predicates:
• A(x) : x is on the board of directors."
• E(x) : x earns more than $100, 000.
• W(x) : x works more than 60 hours per week.
The domain is the set of all employees of a certain company. Match each English statement with its equivalent logical expression.
? v 1. Everyone who works more than 60 hours per week earns more than $100,000.
A. 3x(E(x) ^ ¬W(x))
B. Vx(W(x) → E(x))
C. Ex(¬A(x) → E(x))
D. Vx(W(x) ^ E(x))
E. 3x(¬A(x) ^ E(x))
F. 3x(A(x) ^ ¬E(x)^ W(x))
G. Ex(A(x) V ¬E(x) V W(x))
H. Vx(A(x) → E(x))
I. Vx(A(x) ^ E(x))
2 v 2. Someone on the board of directors does not earn more that $100.000 and works more than 60 hours per week.
? v 3. Every member of the board of directors earns more than $100,000.
2. v 4. There is someone who is not on the board of directors and earns more than $100,000.
? v 5. There is someone who earns more than $100,000, but does not work more than 60 hours per week.

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