value of each ollowing interpretation where the domain consists of people, M(x, y) is "x is the mother of y", F(x) is "x is female", M(x) is "x is male." a. (x)(3)(y, x) b. (x)(Vy)(M(y,x) → M(y)) Which of the following sentences are equivalent to the statement Cats are smarter than dogs. a. Some cats are smarter than some dogs. b. There is a cat that is smarter than all dogs. c. All cats are smarter than all dogs. d. Only cats are smarter than dogs. e. All cats are smarter than any dog. Using the predicate symbols shown and appropriate quantifiers, write each English language statement as a predicate wff. (The domain is the whole world.) B(x): x is a ball R(x): x is round S(x): x is a soccer ball All soccer balls are round. a. b. Some balls are round but soccer balls are not.

value of each ollowing interpretation where the domain consists of people, M(x, y) is "x is the mother of y", F(x) is "x is female", M(x) is "x is male." a. (x)(3)(y, x) b. (x)(Vy)(M(y,x) → M(y)) Which of the following sentences are equivalent to the statement Cats are smarter than dogs. a. Some cats are smarter than some dogs. b. There is a cat that is smarter than all dogs. c. All cats are smarter than all dogs. d. Only cats are smarter than dogs. e. All cats are smarter than any dog. Using the predicate symbols shown and appropriate quantifiers, write each English language statement as a predicate wff. (The domain is the whole world.) B(x): x is a ball R(x): x is round S(x): x is a soccer ball All soccer balls are round. a. b. Some balls are round but soccer balls are not.

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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What is the Truth value of the Expression ∀ (x)P(x) in each of the following interpretation? P(x) is the property that X is yellow, and the domain of interpretation is the collection of all buttercups. P(x) is the property that x is yellow, and the domain of interpretation is the collection of all flowers. P(x) is the property that x is plant, and the domain of interpretation is the collection of all flowers. P(x) is the property that x is either positive or negative , and the domain of interpretation
Give the truth value of each of the following wffs in the interpretation where the domain consists of the states of the United States, Q(x, y) is “x is north of y," P(x) is "x starts with the letter M," and a is "Massachusetts." a. (Vx)P(x) b. (Vx)(Vy)(Vz)[Q(x, y) ^ Q(y, z) → Qx, z)] c. Ay)Ex)Q(y, x) d. (Vx)Ay)[P(y) Qx, y)] e. (dy)Q(a, y) f. Ax)[P(x) ^ Q(x, a)]
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