HW 4: Functions and Relations

Introduction

In this homework you will gain practice working with functions and relations.

Exercises

1. Problem 4.14 from the text.
2. Problem 4.18 from the text. Be sure to explain your answers.
3. Problem 4.19 from the text.
4. Problem 4.26. (Note: In part d, the hypothesis that f is total does not provide any new information, since we (our class) are only working with total functions.)
5. Problem 4.29 from the text.
6. Problem 4.36 from the text.
7. Which of the following relations on the set of all people are equivalence relations? Determine the propertied of an equivalence relation that the others lack.
   1. {(a, b) | a and b have the same age}
   2. {(a, b) | a and b have the same parents}
   3. {(a, b) | a and b share a common parent}
   4. {(a, b) | a and b have met}
   5. {(a, b) | a and b speak a common language}
8. Let R be the relation consisting of all pairs (x, y) such that x and y are strings of uppercase and lowercase English letters with the property that for every positive integer n, the nth characters in x and y are the same letter, either uppercase or lowercase. Show that R is an equivalence relation.
9. Let R be the relation on the set of ordered pairs of positive integers such that (a, b) R (c, d) IFF ad = bc. Show that R is an equivalence relation.

Submit

When you are done, submit the .pdf file on Moodle.