Math 360, Fall 2014, 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. Anti-symmetric relation.
6. Transitive relation.
7. Partial order.
8. Equivalence relation.
9. Partition (of a set).
10. Cell (of a partition).

Solve the following problems:

1. Section 0, problems 1, 5, 7, 11, and 12.

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