Page 27 - Probability and Statistical Inference

4 1. Nations of Probability

all proper subsets of S. It is obvious that A is a proper subset of B, but A is
not a subset of either C or D. !
Suppose that A and B are two subsets of S. Now, we mention some custom-
ary set operations listed below:

Figure 1.2.1. Venn Diagrams: Shaded Areas
Correspond to the Sets (a) A ∩ B (b) A ∪ B
c

Figure 1.2.2. Venn Diagrams: Shaded Areas
Correspond to the Sets (a) A ∩ B (b) A ∆ B

The union and intersection operations also satisfy the following laws: For
any subsets A, B, C of S, we have

We say that A and B are disjoint if and only if there is no common element
between A and B, that is, if and only if A ∩ B = ϕ, an empty set. Two disjoint
sets A and B are also referred to as being mutually exclusive.