You & maths

## The Foundations: Logic and Proofs – Exercises from 21 to 25

21. 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 … Read more The Foundations: Logic and Proofs – Exercises from 21 to 25

## The Foundations: Logic and Proofs – Exercises from 16 to 20

16. 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 … Read more The Foundations: Logic and Proofs – Exercises from 16 to 20

## The Foundations: Logic and Proofs – Exercises from 11 to 15

11. Let p and q be the propositions “Swimming at the New Jersey shore is allowed” and “Sharks have been spotted near the shore,” respectively. Express each of these compound propositions as an English sentence. a) ¬q                          b) p ∧ q                     c) ¬p ∨ q d) p → ¬q                  e) ¬q → … Read more The Foundations: Logic and Proofs – Exercises from 11 to 15

## The Foundations: Logic and Proofs – Exercises from 6 to 10

6. What is the negation of each of these propositions?   a) Jennifer and Teja are friends. b) There are 13 items in a baker’s dozen. c) Abby sent more than 100 text messages yesterday. d) 121 is a perfect square. Answer:   a) Jennifer and Teja are not friends. The opposite of a statement … Read more The Foundations: Logic and Proofs – Exercises from 6 to 10

## The Foundations: Logic and Proofs – Exercises from 1 to 5

1. Which of these sentences are propositions? What are the truth values of those that are propositions? a) Boston is the capital of Massachusetts. b) Miami is the capital of Florida. c) 2 + 3 = 5. d) 5 + 7 = 10. e) x + 2 = 11. f) Answer this question. Answer: a) … Read more The Foundations: Logic and Proofs – Exercises from 1 to 5