1.2 Review of Set Notation

Since sample spaces and events use the language of sets, we recall in this section some basic definitions, notation, and properties of sets.

Let ? be a set of points. If ? is a point in ?, we write ? ? ?. Let A and B be two collections of points in ?. If every point in A also belongs to B, we say that A is a subset of B, and we denote this by writing A ? B. If A ? B and B ? A, then we write A = B; i.e., two sets are equal if they contain exactly the same points. If A ? B but A ? B, we say that A is a proper subset of B.

Set relationships can be represented graphically in Venn diagrams. In these pictures, the whole space ? is represented by a rectangular region, and subsets of ? are represented by disks or oval-shaped regions. For example, in Figure 1.7(a), the disk A is completely contained in the oval-shaped region B, thus depicting the relation A ? B.

Figure 1.7: (a) Venn diagram of A ? B. (b) The complement of the disk A, denoted by A ^c, is the shaded part of the diagram.