## Try It Now

Work these exercises to see how well you understand this material.

### Exercises

- List all partitions of the set A = {a, b, c}.
- A student, on an exam paper, defined the term partition the following way: “Let A be a set. A partition of A is any set of nonempty subsets A
_{1}, A_{2}, A_{3}, . . . of A such that each element of A is in one of the subsets.” Is this definition correct? Why? - Show that {{2n| n ∈ ℤ},{2n+ 1 | n ∈ ℤ}} is a partition of ℤ. Describe this partition using only words.
- A survey of 90 people, 47 of them played tennis and 42 of them swam. If 17 of them participated in both activities, how many of them participated in neither?
- Regarding the Theorem 2.3.9,
- (a) Use the two set inclusion-exclusion law to derive the three set inclusion- exclusion law. Note: A knowledge of basic set laws is needed for this exercise.
- (b) State and derive the inclusion-exclusion law for four sets.

- The definition of ℚ = {a/b| a, b ∈ ℤ, b ≠ 0} given in Chapter 1 is awkward. If we use the definition to list elements in ℚ, we will have duplications such as , , and . Try to write a more precise definition of the rational numbers so that there is no duplication of elements.

Source: Al Doerr and Ken Levasseur, http://faculty.uml.edu/klevasseur/ads-latex/ads.pdf

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