3-5 Working With Sets

Quick Review

The complement of a set A is the set of all elements in the universal set that are not in A.

Example

Suppose U = {1, 2, 3, 4, 5, 6} and Y = {2, 4, 6}. What is Y'?

The elements in U that are not in Y are 1, 3, and 5.

So Y' = {1, 3, 5}.

Exercises

List all the subsets of each set.

38. {s, t}
39. {5, 10, 15}
40. How do you write “A is the set of even whole numbers that are less than 18” in roster form? How do you write A using set-builder notation?
41. Suppose U = {1, 2, 3, 4, 5, 6, 7, 8} and B = {2, 4, 6, 8}. What is B'?

3-6 Compound Inequalities

Quick Review

Two inequalities that are joined by the word and or the word or are called compound inequalities. A solution of a compound inequality involving and makes both inequalities true. A solution of an inequality involving or makes either inequality true.

Example

What are the solutions of − 3 ≤ z − 1 < 3 ? negative 3 less than or equal to bold z minus 1 less than 3 question mark

− 3 ≤ z − 1 < 3   − 2 ≤ z < 4 Add  1  to each part of the inequality  . table with 2 rows and 3 columns , row1 column 1 , negative 3 , column 2 less than or equal to z minus 1 less than 3 , column 3 , row2 column 1 , negative 2 , column 2 less than or equal to z less than 4 , column 3 cap add , 1 . toeachpartoftheinequality . . , end table

Exercises

Solve each compound inequality.

42. − 2 ≤ d + 1 2 < 4 1 2 negative 2 less than or equal to d plus , 1 half , less than 4 , and 1 half
43. 0 < − 8 b ≤ 12 0 less than negative 8 b less than or equal to 12
44. 2 t ≤ − 4  or  7 t ≥ 49 2 t less than or equal to negative 4 , or , 7 t greater than or equal to 49
45. 5 m < − 10  or  3 m > 9 5 m less than negative 10 , or , 3 m greater than 9
46. − 1 ≤ a − 3 ≤ 2 negative 1 less than or equal to eh minus 3 less than or equal to 2
47. 9.1 > 1.4 p ≥ − 6.3 9.1 greater than 1.4 p greater than or equal to negative 6.3
48. Climate A town's high temperature for a given month is 88°F and the low temperature is 65°F. Write a compound inequality to represent the range of temperatures for the given month.

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