Math 360, Fall 2019, Assignment 2

No doubt many people feel that the inclusion of mathematics among the arts is unwarranted. The strongest objection is that mathematics has no emotional import. Of course this argument discounts the feelings of dislike and revulsion that mathematics induces....

- Morris Kline, Mathematics in Western Culture

Carefully define the following terms, then give one example and one non-example of each:

1. Binary relation (on a set $A$).
2. Reflexive (binary relation).
3. Symmetric (binary relation).
4. Transitive (binary relation).
5. Equivalence relation.
6. Equivalence class (of an element $a\in A$, with respect to an equivalence relation $\sim$ on $A$; also known as $\left[a\right]_\sim$).
7. Partition (of a set $A$).
8. Function (from $A$ to $B$).
9. Domain (of a function).
10. Codomain (of a function).
11. Image (of a function).
12. Injective (function; a.k.a. one-to-one function).
13. Surjective (function; a.k.a. onto function).
14. Bijective (function).

Carefully state the following theorems (you do not need to prove them):

1. Theorem relating equivalence relations to partitions.

Solve the following problems:

1. Section 0, problems 12, 23, 25, 29, 30, 31, and 32.

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