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 130: 27


a. The statement says that there are a circle and a square with the property that the circle is above the square and has a different color from the square. This statement is true. For example, circle a lies above square e and is differently colored from e. (Several other examples could also be given.) b. Negation: $\forall$ circles x and $\forall$ squares y, x is not above y or x and y have the same color.

Work Step by Step

Recall the negation of an exists statement: ~($\exists x$ in D, P(x)) $\equiv \forall x$ in D such that ~P(x). To negate a multiply quantified statement, apply the laws in stages moving left to right along the sentence.
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