Discrete Mathematics and Its Applications, Seventh Edition

Published by McGraw-Hill Education
ISBN 10: 0073383090
ISBN 13: 978-0-07338-309-5

Chapter 1 - Section 1.1 - Propositional Logic - Exercises: 2

Answer

a. Not a proposition. b. Not a proposition. c. Proposition; false. d. Not a proposition. e. Proposition; false f. Not a proposition.

Work Step by Step

A proposition is a declarative sentence (that is, a sentence that declares a fact) that is either true or false, but not both. Propositions must have clear truth values, so cannot contain free variables. a. Imperative, not a declarative sentence. b. A question, not a declarative sentence. c. A declarative sentence which contradicts a known fact and therefore, a proposition which is false. d. A declarative sentence whose truth value depends on the free variable x (true for x = 1 and false for all other values of x) and therefore, not a proposition. e. A declarative sentence which contradicts a known fact and therefore, a proposition which is false. A declarative sentence whose truth value depends on the free variable n and therefore, not a proposition.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.