Geometry: Common Core (15th Edition)

Published by Prentice Hall
ISBN 10: 0133281159
ISBN 13: 978-0-13328-115-6

Chapter 2 - Reasoning and Proof - 2-4 Deductive Reasoning - Got It?: 3

Answer

a) conclusion: The Nile is the longest river in the world. b) It does not matter.

Work Step by Step

a) The Law of Syllogism lets us conclude: If a river is more than 4000 miles long, then it is the longest river in the world. Since the given statement about the Nile matches the hypothesis of the new conditional, we can conclude that the Nile is the longest river in the world. b) The order does not matter. Use the same example with the Law of Detachment first. Since the given statement about the Nile matches the hypothesis of the first conditional, we can conclude that the Nile is longer than the Amazon. This can be stated as a conditional: If a river is the Nile, then it is longer than the Amazon. We now have two conditionals to which we can apply the Law of Syllogism: If a river is the Nile, then it is longer than the Amazon. If a river is longer than the Amazon, then it is the longest river in the world. Since the first conclusion matches the second hypothesis the Law of Syllogism let's us conclude: If a river is the Nile, then it is the longest river in the world. This matches our conclusion in part a, where we applied the laws in the opposite order.
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