Logout Open In App
Open In App
Warning: foreach() argument must be of type array|object, bool given in /var/www/html/web/app/themes/studypress-core-theme/template-parts/header/mobile-offcanvas.php on line 20

Chapter 1: Q1.1-19E (page 14)

For each of these sentences, determine whether an inclusive or, or an exclusive or, is intended. Explain your answer

a) Coffee or tea comes with dinner.
b) A password must have at least three digits or be at least eight characters long.
c) The prerequisite for the course is a course in number theory or a course in cryptography.
d) You can pay using U.S. dollars or euros

Short Answer

Expert verified

a) Exclusive or

b) Inclusive or

c) Inclusive or

d) Exclusive or

Step by step solution

01

Exclusive or and inclusive or

“Exclusive or” means “either this or that, but not both of them.”

“Inclusive or” means “either this, or that, or both of them.”

02

Exclusive or is intended in a)

Coffee or tea comes with dinner.

One of coffee or tea can be served with dinner.

Hence, exclusive or is intended.

03

Inclusive or is intended in b)

A password must have at least three digits or be at least eight characters long.

Password can have digits and characters together.

Hence, inclusive or is intended.

04

Inclusive or is intended in c)

The prerequisite for the course is a course in number theory or a course in cryptography.

Student should pass either of number theory or cryptography. It is possible that he /she passes both.

Hence, inclusive or is intended.

05

Truth value for d)

You can pay using U.S. dollars or euros.

You can’t pay using both U.S. dollars and euros.

Hence, exclusive or is intended.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

You are eligible to be President of the U.S.A. only if you are at least 35 years old, were born in the U.S.A, or at the time of your birth both of your parents were citizens, and you have lived at least 14 years in the country. Express your answer in terms of e: “You are eligible to be President of the U.S.A.,” a: “You are at least 35 years old,” b: “You were born in the U.S.A,” p: “At the time of your birth, both of your parents where citizens,” and r: “You have lived at least 14 years in the U.S.A.”

Let P(x,y)be the statement “Student xhas taken class y,” where the domain for both xconsists of all students in your class and for yconsists of all computer science courses at your school. Express each of these quantifications in English.

(a) ∃x∃yP(x,y) (b) ∃x∀yP(x,y)

(c) ∀x∃yP(x,y) (d) ∃y∀xP(x,y)

(e) ∀y∃xP(x,y) (f) ∀x∀yP(x,y)

Let p and q be the propositions “The election is decided” and “The votes have been counted,” respectively. Express each of these compound propositions as an English sentence.

a)¬p

b)p∨q

c)¬p∧q

d)q→p

e)¬q→¬p

f )¬p→¬q

g) p↔q

h) ¬q∨(¬p∧q)

What is the negation of each of these propositions?

a) Mei has an MP3 player.

b) There is no pollution in New Jersey.

c)2+1=3

d) The summer in Maine is hot and sunny

Let p, q, and r be the propositions p : You get an A on the final exam. q : You do every exercise in this book. r : You get an A in this class. Write these propositions using p, q, and r and logical connectives (including negations).

a)You get an A in this class, but you do not do every exercise in this book.

b) You get an A on the final, you do every exercise in this book, and you get an A in this class.

c) To get an A in this class, it is necessary for you to get an A on the final.

d) You get an A on the final, but you don’t do every exercise in this book; nevertheless, you get an A in this class.

e) Getting an A on the final and doing every exercise in this book is sufficient for getting an A in this class.
f ) You will get an A in this class if and only if you either do every exercise in this book or you get an A on the final.
See all solutions

Recommended explanations on Math Textbooks

Applied Mathematics

Read Explanation

Calculus

Read Explanation

Logic and Functions

Read Explanation

Mechanics Maths

Read Explanation

Geometry

Read Explanation

Decision Maths

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free