Book edition 7th

Author(s) Kenneth H. Rosen

Pages 808 pages

ISBN 9780073383095

Answers without the blur.

Just sign up for free and you're in.

Short Answer

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.

a) $r \land \neg q$

b) $p \land q \land r$

c) $r \to p$

d) $p \land \neg q \land r$

e) $(p \land q) \to r$

f) $r \leftrightarrow (p \lor q)$

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step1: Definition of proposition

Proposition:
1. It is a declarative statement which can be either true or false. 2. It cannot be both true and false simultaneously

Step 2: Proposition using p, q and r for a)

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.

You get an A in this class, but you do not do every exercise in this book. The above given statement means $r \land \neg q$ .

Step 3:Proposition using p and q for b)

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

The given statement means $p \land q \land r$

Step 4: Proposition using p, q and r for c)

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

The above given statement means $r \to p$

Step 5: Proposition using p, q and r for d)

You get an A on the final, but you don’t do every exercise in this book; never the less, you get an A in this class

The given statement means $p \land \neg q \land r$ .

Step 6: Proposition using p, q and r for e)

Getting an A on the final and doing every exercise in this book is sufficient for getting an A in this class.

The given statement means $(p \land q) \to r$ .

Step 7: Proposition using p, q and r for 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.

The given statement means $r \leftrightarrow (p \lor q)$

Find Study Materials for

Create Study Materials

Select your language

Discrete Mathematics and its Applications

Answers without the blur.

Short Answer

Step by Step Solution

Step1: Definition of proposition

Step 2: Proposition using p, q and r for a)

Step 3:Proposition using p and q for b)

Step 4: Proposition using p, q and r for c)

Step 5: Proposition using p, q and r for d)

Step 6: Proposition using p, q and r for e)

Step 7: Proposition using p, q and r for f)

Most popular questions for Math Textbooks

Want to see more solutions like these?

Recommended explanations on Math Textbooks

Select your language

Discrete Mathematics and its Applications

Answers without the blur.

Short Answer

Step by Step Solution

Step1: Definition of proposition

Step 2: Proposition using p, q and r for a)

Step 3:Proposition using p and q for b)

Step 4: Proposition using p, q and r for c)

Step 5: Proposition using p, q and r for d)

Step 6: Proposition using p, q and r for e)

Step 7: Proposition using p, q and r for f)

Most popular questions for Math Textbooks

Want to see more solutions like these?

Recommended explanations on Math Textbooks

Decision Maths

Calculus

Probability and Statistics

Statistics

Mechanics Maths

Geometry

Pure Maths