Consider a collection of elements called a set. The plane is a set; the real line is a set; a point is a set; the unit interval is a set. Sets can also be listed as collections of elements, e.g., S ₁ = {1, 4, 9} and S ₂ = {cow, chicken, pig} are both sets. The collection of these sets is also a set, i.e., { , , [0, 1]} is a set. Given two sets A and B, A is said to be a subset of B (denoted A ? B) if every element of A is also an element of B. Of the two examples above, S ₁ is a subset of the set of positive integers and S ₂ is a subset of the set of animals.

Given A ? B, the complement of A in B (denoted B\ A)is defined to be all of the elements of B that are not in A, i.e.,

The union of A and B (denoted A ? B) is to be the set of points that is in either A or B, i.e.,

The intersection of A and B (denoted A ? B) is defined to be the set of all points that are in both A and B, i.e.,

For the remainder of this appendix we...