Thinking Mathematically (6th Edition)

Published by Pearson
ISBN 10: 0321867327
ISBN 13: 978-0-32186-732-2

Chapter 3 - Logic - 3.8 Arguments and Euler Diagrams - Exercise Set 3.8 - Page 204: 46

Answer

The example is Cats are birds. Birds are mammals. Therefore, cats are mammals.

Work Step by Step

When the Euler diagram is drawn for the premises and the conclusion, then the argument is valid if and only if every possible diagram illustrates the conclusion of the argument. Now, take the example in which the premises are false but the conclusion is true. Example: Cats are birds. Birds are mammals. Therefore, cats are mammals. In this example, premises and the conclusion are Premise : Cats are birds. Premise : Birds are mammals. Conclusion: Cats are mammals. Both premises are false. But the conclusion is true. Diagram for the premise is:
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