1. Chapter 8 Unit Question How do inequalities affect algebraic concepts?

2. Open Learning Logs Place date on Left…Section 8 – 2 on right

3. WARM UP 8 – 2 Let A = the set of people whose first AND last names begin with a vowel and B = the set of people whose first OR last name begins with a vowel. 1.Name at least one person in each set. If you cannot think of anyone, make up a name 2.Which set do you think will have more members? Why?

4. Section 2 How do we perform set operations?

5. Homework Check

6. Union Definition… Elements that are in EITHER or BOTH sets If you see a number, it is in the Union!, Elements that are in BOTH sets Intersection Definition… You MUST see a number twice, to be in the Intersection!

7. Venn Diagram Elements in both sets are written here Elements of the first set, but not in the second, are written here Elements of the second set, but not in the first, are written here The union is everything you seeThe intersection is the stuff in the middle

8. Set A = { 1, 3, 5, 7} Set B = {2, 3, 4, 5} AB 3535 1717 2424 The union…(everything you see) A U B = The intersection… (stuff in the middle) A ∩ B = { 1, 2, 3, 4, 5, 7 } { 3, 5 }

9. Set C = { Alan, Brett, Carl} Set D = {Brett, Colin, Dave} CD Brett Alan Carl Colin Dave The union…(everything you see) C U D = The intersection… (stuff in the middle) C ∩ D = { Alan, Brett, Carl, Colin, Dave } { Brett }

10. Set E = { Odd whole number less than 10 } Set F = { Even whole numbers less than 10 } EF 1739517395 26482648 The union…(everything you see) E U F = The intersection… (stuff in the middle) E ∩ F = { 1, 2, 3, 4, 5, 6, 7, 8, 9 }{ } or Ф Called the EMPTY Set or the NULL Set

11. Graphing Intersections… An intersection is an “AND” statement. For example… x ≥ 3 and x < 5 Graph using Real Numbers Both conditions must be true! 0 1 2 3 4 5 6 7 1 st plot the points indicated in the statement with the appropriate dots Then do the three tests to see where to draw the line(s)

12. Graphing Unions… A Union is an “OR” statement. For example… y < 2 or y ≥ 6 Graph using Real Numbers Either condition can be true! 0 1 2 3 4 5 6 7 1 st plot the points indicated in the statement with the appropriate dots Then do the three tests to see where to draw the line(s)

13. Graph the solution set… For best results... Use at a temperature at or above 40 degrees AND a temperature below 70 degrees t ≥ 40 and t < 70 Graph using Real Numbers Both conditions must be true! 35 40 45 50 55 60 65 70 75 80 1 st plot the points indicated in the statement with the appropriate dots Then do the three tests to see where to draw the line(s)

14. Summary!!! So, if you see... OPEN DOTS!!!! ≤ or ≥ CLOSED DOTS!!! “AND” Generally… connect the dots “OR” Generally… Arrows point away from each other

15. Support / Refute The Union of two sets will always contain more members than the Intersection of the same two sets.

16. Homework Do HoffmaSheet 8 – 2