A.1 Sets

A set is a collection of objects, called members or elements of the set. When a set is to be referred to more than once, it is convenient to label it, usually, by a capital letter such as A, B,....

There are two distinct ways to describe a set:

1. By listing the elements of the set between curly brackets { }.

2. By giving a rule or characteristic property, which the elements of the set must satisfy.

For example, the set of all even positive integers less than 10 is written as {2, 4, 6, 8} = {6, 2, 8, 4} or

Note that each element of a set is not repeated within the set itself and the order in which the elements of a set are listed is immaterial.

Some definitions and notations are listed as follows:

1. A ? B or B ? A ( A is a subset of B): every element of A is an element of B. A ? B. ( A is a proper subset of B).

2. A = B ( A is equal to B): if and only if A ? B and B ? A.

3. ? ( empty set): the set that contains no elements.

4. x ? A: x is an element of the set A.

5. x ? A: x is not an element...