Thinking Mathematically (6th Edition)

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

Chapter 1 - Problem Solving and Critical Thinking - 1.1 Inductive and Deductive Reasoning - Exercise Set 1.1 - Page 14: 76


Inductive reasoning involves going from a series of specific cases to a general statement. The conclusion is an inductive argument is never guaranteed.

Work Step by Step

Example In order to find the next number in the sequence \[6,13,20,27,...\]. There is more than one correct answer. Here, the sequence again \[6,13,20,27,...\]Look at the difference of each term. \[13-6=7,20-13=7,27-20=7\] Thus, the next term is 34, because \[34-27=7\]. However, what if the sequence represents the dates. Then, the next number could be 3 (31 days in a month). The next number could be 4 (30-day month), or it could be 5 (29-day month – Feb. Leap year)or even 6 (28-day month – Feb.) Deductive reasoning- A type of logic in which one goes from a general statement to a specific instance. The deductivereasoninggoes in the same direction as that of the conditional and links premises with the conclusion. If all premises are true, the term is clear, and the rule of deductive logic is followed, then the conclusion reached is necessarily true. Example: All men are mortal. (major premise), Socrates is a man. (minor premise). Therefore, Socrates is mortal (conclusion). The above is an example of a syllogism.
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