• :00Days
  • :00Hours
  • :00Mins
  • 00Seconds
A new era for learning is coming soonSign up for free
Log In Start studying!

Select your language

Suggested languages for you:
Deutsch (DE)
Deutsch (UK)
Deutsch (US)

Americas

Europe

Answers without the blur. Sign up and see all textbooks for free! → Illustration

Q35E

Expert-verified
Discrete Mathematics and its Applications
Found in: Page 35
Discrete Mathematics and its Applications

Discrete Mathematics and its Applications

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.

Register for Free I’ll do it later
Illustration

Short Answer

Find the dual of each of these compound propositions..

a) p∧¬q∧¬r

b) (p∧q∧r)∧s

c) (p∨F)∧(q∨T)

a) p∨¬q∨¬r

b) (p∨q∨r)∨s

c) (p∧T)∨(q∧F)

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :
TABLE OF CONTENTS

Step1:Definition of dual

The dual of a proposition which contains only the logical operators ∨,∧,¬, is the compound proposition obtained by replacing each ∧ by ∨ , each ∧ by ∨ , each T by , F and each F by T

Step 2: Dual of a)

Dual of p∧¬q∧¬r is . p∨¬q∨¬r

Step 2: Dual of b)

Dual of (p∧q∧r)∧s is (p∨q∨r)∨s

Step 3: Dual of c)

Dual of (p∨F)∧(q∨T) is (p∧T)∨(q∧F)

Most popular questions for Math Textbooks

What is the value of x after each of these statements is encountered in a computer program, if x = 1 before the statement is reached?

a) if x+2=3 then x=x+1 b) if (x+1=3)OR (2x+2=3) then x=x+1 c) if (2x+3=5)AND (3x+4=7) then x=x+1 d) if (x+1=2) XOR (x+2=3) then x=x+1e) if x < 2 thenx=x+1

Write each of these propositions in the form “p if and only if q” in English.

a) If it is hot outside you buy an ice cream cone, and if you buy an ice cream cone it is hot outside. b) For you to win the contest it is necessary and sufficient that you have the only winning ticket. c) You get promoted only if you have connections, and you have connections only if you get promoted. d) If you watch television your mind will decay, and conversely.

e) The trains run late on exactly those days when I take it.

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.”

Show that (p∨q)∧(¬p∨r)→(q∨r) is a tautology

Are these system specifications consistent? “Whenever the system software is being upgraded, users cannot access the file system. If users can access the file system, then they can save new files. If users cannot save new files, then the system software is not being upgraded.”
Icon

Want to see more solutions like these?

Sign up for free to discover our expert answers
Get Started - It’s free

Recommended explanations on Math Textbooks

Decision Maths

Read explanation

Calculus

Read explanation

Probability and Statistics

Read explanation

Statistics

Read explanation

Mechanics Maths

Read explanation

Geometry

Read explanation

Pure Maths

Read explanation

94% of StudySmarter users get better grades.

Sign up for free
94% of StudySmarter users get better grades.