12240/Homework Assignment 4

This assignment is due at the tutorials on Thursday October 18. Here and everywhere, neatness counts!! You may be brilliant and you may mean just the right things, but if the teaching assistants will be having hard time deciphering your work they will give up and assume it is wrong.
Task 0. Add your name to the Class Photo page!
Task 1. Read sections 1.5 through 1.7 in our textbook. Remember that reading math isn't like reading a novel! If you read a novel and miss a few details most likely you'll still understand the novel. But if you miss a few details in a math text, often you'll miss everything that follows. So reading math takes reading and rereading and rerereading and a lot of thought about what you've read.
Task 2. Solve problems 3, 8, 9, 10, and 11 on pages 4142, but submit only your solutions of problems 8, 9, and 11.
Task 3. Solve problems 1, 2, 4, 5, 9, 12, 13, and 16 on page 5356, but submit only your solutions of problems 4, 5, 9, and 12.
Just for Fun (1).

8641 
Just for Fun (2). Is there a problem with the following inductive proof that all horses are of the same color?
We assert that in all sets with precisely horses, all horses are of the same color. For , this is obvious: it is clear that in a set with just one horse, all horses are of the same color. Now assume our assertion is true for all sets with horses, and let us be given a set with horses in it. By the inductive assumption, the first of those are of the same color and also the last of those. Hence they are all of the same color as illustrated below:
(The horses surrounded by round brackets are all of the same color. The horses surrounded by square brackets are all of the same color. Therefore the first and the last horses have the same color as the ones in the middle group, and hence all horses are of the same color.)