In Chapter 3, you investigated some of the activities that involve sets. To extend the previously developed notions, consider that when you define a set, you can define it so that its elements bear relationships with each other. If you investigate a set that consists of numbers that are less than 10 and greater than zero, for example, then you can create a definition along the following lines:

{a | a = 10 ∧ a | a > 0}

This expression reads along the lines of “a such that a is less than 10 and a such that a is greater than 0.” While the numbers 0 and 10 are not part of the set, all the numbers in the set are defined by two common features: They must be greater than 0 and they must be less than 10. As Figure 4.2 illustrates, the features ...

Start Free Trial

No credit card required