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 1.6 - Rules of Inference - Exercises - Page 78: 3

Answer

a) Addition b) Simplification c) Modus Ponens d) Modus Tollens e) Hypothetical Syllogism

Work Step by Step

a) Let us assume: p="Alice is a mathematics major" q="Alice is a computer science major" We can write the given argument using above stated interpretation as: $$p$$$$- - -$$$$p \lor q$$ Using Rule of addition b) Let us assume: p="Jerry is a mathematics major" q="Jerry is a computer science major" We can write the given argument using above stated interpretation as: $$p \land q$$$$- - -$$$$\therefore p$$ Note that the argument uses rule of simplification. c) Let us assume: p="It is rainy" q="pool will be closed" We can write the given argument using above stated interpretation as: $$p \to q$$$$p$$$$- - -$$$$q$$ Note that the argument uses rule of Modus Ponens. d) Let us assume: p="It snows today" q="University is closed" We can write the given argument using above stated interpretation as: $$p \to q $$$$\neg q$$ $$- - -$$ $$\therefore \neg p$$ Note that the argument uses rule of Modus Tollens. e) Let us assume: p="I go swimming" q="I will stay in the sun too long" r="I will sunburn" We can write the given argument using above stated interpretation as: $$p \to q$$$$q \to r$$$$- - - $$$$\therefore p \to r$$ Note that the argument uses rule of Hypothetical Syllogism.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.