Many problems, in diverse areas such as artificial intelligence and circuit design, can be modeled interms of propositional satisfiability.A compound proposition is satisfiable if there is an assignment of truth values to its variables thatmakes it true. For example, pnq is true when p = T and q = T; thus, p aq is satisfiable.When no such assignment exists, the compound proposition is unsatisfiable. a. Explain why if a compound proposition is unsatisfiable, then its negation is a tautology.b. Give an example of an unsatisfiable compound proposition with two variables, p and q.Justify your answer.

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a. Explain why if a compound proposition is unsatisfiable, then its negation is a tautology. b. Give an example of an unsatisfiable compound proposition with two variables, p and q- Justify your answer.

a. Explain why if a compound proposition is unsatisfiable, then its negation is a tautology. b. Give an example of an unsatisfiable compound proposition with two variables, p and q- Justify your answer.

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

Many problems, in diverse areas such as artificial intelligence and circuit design, can be modeled in
terms of propositional satisfiability.
A compound proposition is satisfiable if there is an assignment of truth values to its variables that
makes it true. For example, pnq is true when p = T and q = T; thus, p aq is satisfiable.
When no such assignment exists, the compound proposition is unsatisfiable.

a. Explain why if a compound proposition is unsatisfiable, then its negation is a tautology.
b. Give an example of an unsatisfiable compound proposition with two variables, p and q.
Justify your answer.

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