Discrete Mathematics and Its Applications, Seventh Edition

Published by McGraw-Hill Education
ISBN 10: 0073383090
ISBN 13: 978-0-07338-309-5

Chapter 1 - Section 1.1 - Propositional Logic - Exercises - Page 16: 45

Answer

The truth value of the statement “Fred is not happy" is 0.2 The truth value of the statement “John is not happy" is 0.6

Work Step by Step

The proposition "Fred is not happy" is clearly the negation of the proposition "Fred is happy". Since the truth value of this proposition (in fuzzy logic) is 0.8, and the truth value of the negation is 1 minus the truth value*, this last one is 0.2 The same reasoning applies to the second sentence "John is not happy". *We can think of these truth values in fuzzy logic as measure of the truthness of a proposition: the closer this value to one, the 'truther' the proposition. It is clear then that the higher the truth value of a proposition, the lower has to be the truth value of its negation.
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