# Course:MATH220/Archive/2010-2011/921/Homework

## Homework

### Due Tuesday, May 17th

We discussed in class the Pythagorean theorem, and I provided three proofs of this theorem. We also talked about statements.

Write out the Pythagorean theorem as a statement. Choose whichever of the three proofs you prefer, and being mindful of the suggestions from chapter 0 of the text, write up a more complete proof of this theorem.

### Due Tuesday, May 24th

Do problems 11.1, 11.2, 11.3, 11.4, 11.5 and 11.9 in Chapter 11 of the textbook. Please note that these are not to be refereed at the beginning of class, simply handed in.

### Due Tuesday, May 31st

Read sections 11.3--11.5 in the textbook. Do the following problems.

• 11.26
• 11.27
• 11.28 Hint: Show that there are infinitely many pairs of integers s and t such that $sa+tb=0$ .
• 11.34
• 11.36 Hint: Consider how we proved that ${\sqrt {p}}$ is irrational.
• 11.37
• 11.38a

Solutions: File:Soln3.pdf

### Due Thursday, June 9th

Read sections 2.1--2.5 of the textbook. These talk about logic (implications, and/or), and while we have been using these liberally so far, it would be useful to go back now and read more about them.

Do the following problems. These are all relatively short but are there to help you get used to sets.

1.3, 1.5, 1.6, 1.8, 1.10, 1.13, 1.14, 1.15, 1.16, 1.18, 1.19, 1.24, 1.27, 1.41, 1.42, 1.44, 1.46

Prove De Morgan's laws.

Theorem (De Morgan) Let A, B be sets. Then we have the following equalities.

$(A\cup B)^{c}=A^{c}\cap B^{c}\qquad {\text{and}}\qquad (A\cap B)^{c}=A^{c}\cup B^{c}$ Draw Venn diagrams of both of these.

Solutions are here File:Soln4.pdf.

### Due Thursday, June 16

Do the following exercises:

9.11, 9.13, 9.14, 9.15, 9.18, 9.19, 9.20, 9.21, 9.24, 9.25, 9.29

Solutions: File:Soln5.pdf

We will also begin on Tuesday, June 14th, the refereeing process. The first problem is up here.

### Due Thursday, June 23rd

Do the following problems.

10.2, 10.3, 10.4, 10.6, 10.8, 10.10, 10.14, 10.15, 10.18, 10.19, 10.22

The second to-be-refereed problem is here.

The solutions to these problems are here File:Soln6.pdf

### Due Thursday, June 30th

Do the following problems:

6.5, 6.6, 6.7, 6.10, 6.14, 6.17, 6.18, 6.20, 6.22, 6.25, 6.32, 6.34, 6.36

The solutions to this assignment are here. File:Soln7.pdf

The third to-be-refereed problem is here. This is due in class for refereeing on Tuesday, June 28th.

### Due Tuesday, July 19th

Do problems

12.1, 12.2, 12.3, 12.4, 12.6, 12.7, 12.8, 12.9, 12.10.

The solutions to this are behind this finely-crafted link: File:Soln8.pdf

The last to-be-refereed problems are here.