Let P(x) be the statement "x can speak Russian" and let Q(x) be the statement "x knows the computer language C++." Express each of these sentences in terms of P(x), Q(x), quantifiers, and logical connectives. The domain for quantifiers consists of all students at your school. a) There is a student at your school who can speak Rus- sian and who knows C++. b) There is a student at your school who can speak Rus- sian but who doesn't know C++. c) Every student at your school either can speak Russian or knows C++. d) No student at your school can speak Russian or knows C++.

Let P(x) be the statement "x can speak Russian" and let Q(x) be the statement "x knows the computer language C++." Express each of these sentences in terms of P(x), Q(x), quantifiers, and logical connectives. The domain for quantifiers consists of all students at your school. a) There is a student at your school who can speak Rus- sian and who knows C++. b) There is a student at your school who can speak Rus- sian but who doesn't know C++. c) Every student at your school either can speak Russian or knows C++. d) No student at your school can speak Russian or knows C++.

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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Let P(x) be the statement “x can speak Russian” and let Q(x) be the statement “x knows C++”. Express each of these statements in terms P(x), Q(x), quantifiers and logical connectives. The domain for quantifiers consists of all students at Mines. There is a student at Mines who can speak Russian and who knows C++. Every student at your school either can speak Russian or knows C++.
Consider a First-Order Logic (FOL) language L with two unary predicate symbols P and Q, one unary function f, and two constants a and b. The following KB has been specified in this language (note that I use directly "for all" to stand for the logical quantifier of "for-all"). 1. (forall x)(Q(x) -> P(x)) (Note: the sentence is logically equivalent to (forall x) (~ Q(x) \/ P(x))).2. P(b)3. Q(b) 4. Q(f(a)) 5. P(f(b)) Consider an interpretation of <D, I>, where D={d1, d2, d3}, and d1 is denoted by a, d2 is denoted b. For the function f, I(f,d1)=d2, I(f,d2)=d3, I(f,d3)=d1. and I(P)={d1, d2}, I(P)={d1, d2}. Is this interpretation a model of L?
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