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 3.3 - Page 129: 6

Answer

The statement says no matter what square anyone may give you, you can find a circle that is of a different color and above that square. This statement is true. Circle c is blue and above squares e, g, and h which are black or grey. Circle b is above square j which is blue. Hence for all squares x in the domain, there exists a circle y such that x and y have difference colors and y is above x.

Work Step by Step

Recall if you want to establish the truth of a statement of the form: ∀x∈D,∃y such that P(x,y), your challenge is to allow someone else to pick whatever element x in D they wish and then you must find an element y in E that "works for that particular x.
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