Discrete Mathematics with Applications 4th Edition

Published by Cengage Learning
ISBN 10: 0-49539-132-8
ISBN 13: 978-0-49539-132-6

Chapter 3 - The Logic of Quantified Statements - Exercise Set 3.4 - Page 144: 28

Answer

3) If an object is gray, then it is a circle. 2) If an object is a circle, then it is to the right of all the blue objects. 1) If an object is to the right of all the blue objects, then it is above all the triangles.

Work Step by Step

1- We switch the 3rd statement to the contrapositive form so it is easier to understand, since the conclusion is "If an object is gray". So, we get If an object is gray, then it is a circle. 2- Rewrite in the form if/then. For the first statement, we can change it into : " If an object is to the right of all the blue objects, then it is above all triangles." 3- Rewrite the statement this way to see the links : 1) If an object is to the right of all the blue objects --> it is above all triangles. 2) If an object is a circle--> it is to the right of all the blue objects. 3) If an object is gray--> it is a circle. 4- We can now observe that it has validity of universal transitivity by rearranging it to the right order. 3) If an object is gray, then it is a circle. 2) If an object is a circle, then it is to the right of all the blue objects. 1) If an object is to the right of all the blue objects, then it is above all the triangles.
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.