Nature of Mathematics - 12th Edition

Problems 1-2

Problems 1-2
There are many problems throughout the text labeled IN YOUR OWN WORDS.

Make sure you understand the operations of union, intersection, and complment (Problem 1).

Problem 2 is interesting because it is taken from the California Assessment Program. It is based on the formula for the cardinality of the union of two sets. Relax; do not be afraid answer using your own words.

Make sure you understand the operations of union, intersection, and complement (Problem 1).

Problem 3 and 4

Problem 3 Remember intersection is "and", union is "or," and complement is "not."
Problem 4 You should remember both of these formulas.

Problems 5-18

Problems 5, 7, 10, and 15
These are unions; to find the union of two sets list all of the elements either of the given sets. If an element is contined in both sets (such as 6 and 8 in Problem 5), list that element only once.

Problems 6, 8, 9, and 16
These are intersections; to find the intersection of two sets list all of the elements that are in both of the given sets.

Problems 11-14 and 17-18
These are complements; to find the complement of a set, look at the universe
(set U), and list all elements in the universe that are not in the given set. Notice that Problems 13 and 18 are the same, and so are Problems 14 and 17.

Problems 19-28

Problems 19, 21, 26, and 27
These are unions; to find the union of two sets first list all of the elements in the given sets using rosters, and then select those elements that are in either of the given sets. Remember, the empty set is { }.

Problems 20, 22, 25, and 28
These are intersections; to find the intersection of two sets first list all of the elements in the given sets using rosters, and then select those elmeents that are in both of the given sets. Remember, the empty set is { }.

Problems 23-24
These are complements; the universe and empty sets are complements.

Problems 29-44

See Example 2.

Problems 29, 31, 34, 41, and 43
These are unions; to find the union of two sets first list all of the elements in the given sets using rosters, and then select those elements that are in either of the given sets.

Problems 30, 32, 33, 42 and 44
These are intersections; to find the intersection of two sets first list all of the elements in the given sets using rosters, and then select those elmeents that are in both of the given sets.

Problems 35-40
These are complements; remember, complement is relative to the universe.

Problems 45-48

See Figure 2.7.

Problems 49-52

See Example 1 for union and intersection; and Figure 2.2 for complement.

Problems 53-58

See Example 3.
Draw two interlocking circles within a rectangle representing the universe. Next, label the circles and fill in the number in the intersection first. Finally, fill in the number in the remaining regions by using subtraction.