1. Section 2.6 Set Operations and Compound Inequalities

2. Introduction In this section we resume our discussion of compound inequalities, particularly those using the conjunctions “and” & “or” We also briefly discuss sets and set operations.

3. Sets A set is a collection of objects. Sets are usually named with capital letters, and the objects in the set (elements) are enclosed within set braces. A = {1, 2, 3, 4} Set A contains the elements 1, 2, 3, and 4. The empty set is a set with no elements. We use { } or Ø to represent the empty set.

4. Set Operations The intersection of sets A and B is the set that contains all the elements that can be found in both A and B. Words associated with intersection: and, both, common, overlap.

5. Continued The union of sets A and B is the set that contains all the elements that can be found in either A or B. Words associated with union: or, either, everything.

6. Examples Suppose that Find

7. Compound Inequalities “and” means intersection. Think: blue yellow = green “or” means union. Think: blueyellow = blue, yellow, and green

8. Helpful tips First determine if you are being asked for union or intersection. If the inequalities need to be solved, solve them. Use the graphs and the “color” rules to determine your solution graph. Write your final solution in interval notation.

9. Graph and write your solution in interval notation: x 0 3x + 2 < -7 or -2x + 1 < 9 -3x < 3 and x + 2 < 6 x > 1 or x > 8