Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
14. Let the following statements be given. p = "Andy is hungry." q = "The refrigerator is empty." r = "Andy is mad." (a) Use connectives to translate the following statement into formal logic. If Andy is hungry and the refrigerator is empty, then Andy is mad. (b) Construct a truth table for the statement in part (a). (c) Suppose that the statement given in part (a) is true, and suppose also that Andy is not mad and the refrigerator is empty. Is Andy hungry? Explain how to justify your answer using the truth table.

14. Let the following statements be given. p = "Andy is hungry." q = "The refrigerator is empty." r = "Andy is mad." (a) Use connectives to translate the following statement into formal logic. If Andy is hungry and the refrigerator is empty, then Andy is mad. (b) Construct a truth table for the statement in part (a). (c) Suppose that the statement given in part (a) is true, and suppose also that Andy is not mad and the refrigerator is empty. Is Andy hungry? Explain how to justify your answer using the truth table.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
See similar textbooks
icon
Related questions
Question

question 14 

14. Let the following statements be given. (a) Use connectives to translate the following statement into formal logic. If Andy is hungry and the refrigerator is empty, then Andy is mad. p="Andy is hungry." q = "The refrigerator is empty." r = "Andy is mad." (b) Construct a truth table for the statement in part (a). (c) Suppose that the statement given in part (a) is true, and suppose also that Andy is not mad and the refrigerator is empty. Is Andy hungry? Explain how to justify your answer using the truth table. 15. Let A be the statement p→ (q^ r). Let B be the statement q → r. (a) Construct truth tables for A and B. (b) Suppose statements A and B are both true. What can you conclude about statement p? Explain your answer using the truth table. 16. Use truth tables to prove the following distributive properties for propositional logic. (a) p^ (q v r) is logically equivalent to (p ^ q) v (p^r). (b) pv (q^r) is logically equivalent to (pv q) ^ (p vr). 17. Use truth tables to prove the associative properties for propositional logic. (a) pv (q vr) is logically equivalent to (pv q) v r. (b) p^ (q^r) is logically equivalent to (p ^ q) ^r. 18. Mathematicians say that "statement P is stronger than statement Q" if Q is true whenever P is true, but not conversely. (In other words, "P is stronger than Q" means that P→ Q is always true, but Q→ P is not true, in general.) Use truth tables to show the following. (a) a^ b is stronger than a. (b) a is stronger than a v b. (c) ab is stronger than a v b. (d) b is stronger than a → b. 19. Suppose Q is a quadrilateral. Which statement is stronger? Explain. • Q is a square. • Q is a rectangle. 20. Which statement is stronger? Explain. • Manchester United is the best football team in England. •Manchester United is the best football team in Europe.
Transcribed Image Text:14. Let the following statements be given. (a) Use connectives to translate the following statement into formal logic. If Andy is hungry and the refrigerator is empty, then Andy is mad. p="Andy is hungry." q = "The refrigerator is empty." r = "Andy is mad." (b) Construct a truth table for the statement in part (a). (c) Suppose that the statement given in part (a) is true, and suppose also that Andy is not mad and the refrigerator is empty. Is Andy hungry? Explain how to justify your answer using the truth table. 15. Let A be the statement p→ (q^ r). Let B be the statement q → r. (a) Construct truth tables for A and B. (b) Suppose statements A and B are both true. What can you conclude about statement p? Explain your answer using the truth table. 16. Use truth tables to prove the following distributive properties for propositional logic. (a) p^ (q v r) is logically equivalent to (p ^ q) v (p^r). (b) pv (q^r) is logically equivalent to (pv q) ^ (p vr). 17. Use truth tables to prove the associative properties for propositional logic. (a) pv (q vr) is logically equivalent to (pv q) v r. (b) p^ (q^r) is logically equivalent to (p ^ q) ^r. 18. Mathematicians say that "statement P is stronger than statement Q" if Q is true whenever P is true, but not conversely. (In other words, "P is stronger than Q" means that P→ Q is always true, but Q→ P is not true, in general.) Use truth tables to show the following. (a) a^ b is stronger than a. (b) a is stronger than a v b. (c) ab is stronger than a v b. (d) b is stronger than a → b. 19. Suppose Q is a quadrilateral. Which statement is stronger? Explain. • Q is a square. • Q is a rectangle. 20. Which statement is stronger? Explain. • Manchester United is the best football team in England. •Manchester United is the best football team in Europe.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 4 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,
SEE MORE TEXTBOOKS