Math 360, Fall 2013, Assignment 1

The beginner ... should not be discouraged if ... he finds that he does not have the prerequisites for reading the prerequisites.

- P. Halmos

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

1. Cartesian product (of two sets).
2. Relation (on a set \(A\)).
3. Reflexive relation.
4. Symmetric relation.
5. Transitive relation.
6. Equivalence relation.
7. Partition (of a set).
8. Cell (of a partition).

Solve the following problems:

1. Section 0, problems 1, 5, 7, and 11.

--------------------End of assignment--------------------

Questions:

1.) As a confirmation, because I don't have a hard copy of the book yet, the questions are:

1.) Describe the following set by listing it's elements\[\{x\in\mathbb{R} | x^2=3\}\]

For 5 and 7, decide whether the object described is a set (is well defined). Give an alternative description

5.) \(\{n\in\mathbb{Z}^+ | n \ is \ a \ large\ number\}\)

7.) \(\{n\in\mathbb{Z} | 39 < n^3 < 57\} \)

11.) List the elements in \(\{a,b,c\} x \{1,2,c\}\)

Thank you for your help in advance. --Robert.Moray (talk) 19:06, 6 September 2013 (EDT)