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Q3E

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Discrete Mathematics and its Applications

Found in: Page 22

Book edition 7th

Author(s) Kenneth H. Rosen

Pages 808 pages

ISBN 9780073383095

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Short Answer

You can graduate only if you have completed the requirements of your major and you do not owe money to the university and you do not have an overdue library book. Express your answer in terms of g: “You can graduate,” m: “You owe money to the university,” r: “You have completed the requirements of your major,” and b: “You have an overdue library book.”

The logical proposition of the given statement is determined as,

g\( \to \)(r˄(~m)˄(~b)).

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Introduction to the Concept

The statement is made up of conditionals and conjunctions.

$\lor \to or \land \to and \underset{}{\to} : only if$

Solution Explanation

The given statements are,

g: You can graduate

m:You owe money to the university

r: You have completed the requirements of your major

b:You have an overdue library book

“You can graduate only if you have completed the requirements of your major“says the statement.

“You do not owe money to the university and you do not have an overdue library book”.

The logical proposition statement is given as g\( \to \)(r˄(~m)˄(~b)) .

Most popular questions for Math Textbooks

Show that, $\land, \lor$ and $\neg$ , ∨form a functionally complete collection of logical operators. [Hint: Use the fact that every compound proposition is logically equivalent to one in disjunctive normal form, as shown in Exercise 42.]

To use the wireless network in the airport you must pay the daily fee unless you are a subscriber to the service. Express your answer in terms of w: “You can use the wireless network in the airport,” d: “You pay the daily fee,” and s: “You are a subscriber to the service.”

Write each of these statements in the form “if p, then q” in English. [Hint: Refer to the list of common ways to express conditional statements provided in this section.]

a) I will remember to send you the address only if you send me an e-mail message. b) To be a citizen of this country, it is sufficient that you were born in the United States. c) If you keep your textbook, it will be a useful reference in your future courses. d) The Red Wings will win the Stanley Cup if their goalie plays well. e) That you get the job implies that you had the best credentials. f ) The beach erodes whenever there is a storm. g) It is necessary to have a valid password to log on to the server. h) You will reach the summit unless you begin your climb too late.

Write each of these statements in the form “if p, then q” in English. [Hint: Refer to the list of common ways to express conditional statements provided in this section.]

a) It is necessary to wash the boss’s car to get promoted. b) Winds from the south imply a spring thaw. c) A sufficient condition for the warranty to be good is that you bought the computer less than a year ago. d) Willy gets caught whenever he cheats. e) You can access the website only if you pay a subscription fee. f ) Getting elected follows from knowing the right people. g) Carol gets seasick whenever she is on a boat.

Construct a truth table for $(p \leftrightarrow q) \leftrightarrow (r \leftrightarrow s)$

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