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 1.2 - Applications of Propositional Logic - Exercises - Page 22: 1

Answer

$e \rightarrow a$

Work Step by Step

Let e be the proposition "You can edit a protected Wikipedia entry", and Let a be the proposition "You are an administrator". We want to translate the statement "You cannot edit a protected Wikipedia entry unless you are an administrator" into propositional logic. First, we will rephrase our statement to emphasize the logical connectives used in the statement. "It is not the case that you can edit a protected Wikipedia entry unless you are an administrator." Now, we can begin to symbolize our sentence as $\lnot e$ unless $a.$ Recall that for two propositions $p$ and $q$, $p\rightarrow q$ can be express in english as $q$ unless $\lnot p.$ Thus $\lnot e$ unless $a$ is $\lnot a \rightarrow \lnot e$, or, equivalently, $e \rightarrow a$
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