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

Chapter 1: The Foundations: Logic and Proofs

Expert-verified
Discrete Mathematics and its Applications
Pages: 1 - 111
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

429 Questions for Chapter 1: The Foundations: Logic and Proofs

  1. Use truth tables to verify these equivalences

    Found on Page 34

  2. Let p be the proposition “I will do every exercise in this book” and q be the proposition “I will get an “A” in this course.” Express each of these as a combination of p and q.

    Found on Page 111

  3. Show that ¬¬pand pare logically equivalent.

    Found on Page 34

  4. Solve this famous logic puzzle, attributed to Albert Einstein, and known as the zebra puzzle. Five men with different nationalities and with different jobs live in consecutive houses on a street. These houses are painted different colors. The men have different pets and have different favorite drinks. Determine who owns a zeb whose favorite drink is mineral water (which is one of the favorite drinks) given these clues: The Englishman lives in the red house. The Spaniard owns a dog. The Japanese man is a painter. The Italian drinks tea. The Norwegian lives in the first house on the left. The green house is immediately to the right of the white one. The photographer breeds snails. The diplomat lives in the yellow house. Milk is drunk in the middle house. The owner of the green house drinks coffee. The Norwegian’s house is next to the blue one. The violinist drinks orange juice. The fox is in a house next to that of the physician. The horse is in a house next to that of the diplomat.

    Found on Page 24

  5. Freedonia has fifty senators. Each senator is either honest or corrupt. Suppose you know that at least one of the Freedonian senators is honest and that, given any two Freedonian senators, at least one is corrupt. Based on these facts, can you determine how many Freedonian senators are honest and how many are corrupt? If so, what is the answer?

    Found on Page 24

  6. Use truth tables to verify the commutative laws.

    Found on Page 34

  7. Find the output of each of these combinatorial circuits

    Found on Page 24

  8. Construct a combinatorial circuit using inverters, OR gates, and AND gates that produces the output(p∧¬r)∨(¬q∧r)from input bitsand p,q,r

    Found on Page 24

  9. Construct a combinatorial circuit using inverters, OR gates, and AND gates that produces the output¬p∨¬r∧¬q∨¬p∧q∨r from input bits p,qand r

    Found on Page 24

  10. Use truth tables to verify the associative laws.

    Found on Page 34

Related Math Textbooks with Solutions

View all the textbook solutions in Math

94% of StudySmarter users get better grades.

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