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 14: 19

Answer

a) exclusive b) inclusive c) inclusive d) exclusive

Work Step by Step

a) You can $choose$ between coffee and tea, but clearly cannot have $both$ coffee and tea: it is therefore an exclusive or. b) We can imagine that a password that has at least three digits and is at at least eight characters long will be accepted (and even more secure!) so the two conditions are $not$ mutually exclusive: the or is inclusive. c) Clearly it is and inclusive or: nobody will refuse us the aforementioned course because we have taken both a course in number theory $and$ a course in cryptography! That is, the two conditions are $not$ mutually exclusive. d) As in the first question, we can choose between US dollars or euros, but, realistically, we cannot choose both (one currency has to be picked before proceeding with the payment): the conditions $are$ mutually exclusive and so is the or.
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