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: 29

Answer

The reordering is: 2. In contrapositive form: $\forall x$, if x is a square, then x is above all the black objects. 3. $\forall x$, if x is above all the black objects, then x is to the right of all the triangles. 1. $\forall x$, if x is to the right of all the triangles, then x is above all the circles.

Work Step by Step

Universal transitivity: $\forall x, P(x) \rightarrow Q(x).$ $\forall x, Q(x) \rightarrow R(x).$ $\therefore \forall x, P(x) \rightarrow R(x).$
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