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: 30

Answer

The reordering is: 3. $\forall x$, if x is black, then x is a square. 2. In contrapositive form: $\forall x$, if x is a square, then x is above all the gray objects. 4. $\forall x$, if x is above all the gray objects, then x is above all the triangles. 1. $\forall x$, if x is above all the triangles, then x is above all the blue objects. $\therefore$ if x is black, then x is above all the blue objects.

Work Step by Step

Universal transitivity: ∀x,P(x)→Q(x). ∀x,Q(x)→R(x). ∴∀x,P(x)→R(x).
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