1-3 Sets and Domains Goals: 1. Use the operations of union and intersection to find solution sets. 2. Represent solution sets of unions and intersections on number lines and in Venn diagrams.

Intersection of Sets You are reading a police report. It says an accident took place in the intersection of Main Street and Lincoln Avenue. What does that mean?

Intersection of Sets In Algebra, the term intersection has a similar meaning when used with sets. The intersection of sets A and B, written A ∩ B, is the set of elements that are in both A and B.

Intersection of Sets Example: Let A = { 1, 2, 3, 5, 6, 8, 13 } and B = { 1, 3, 4, 6, 7, 11 }. Give the intersection of A and B.

Intersection of Sets: Venn Diagrams Example: Let A = { 1, 2, 3, 5, 6, 8, 13 } and B = { 1, 3, 4, 6, 7, 11 }. Give the intersection of A and B A ∩ B is the region in the middle where the circles intersect. Shade this area.

Union of Sets The union of sets A and B, written A U B, is the set of elements that are in either A or B (or both). Write each number only once.

Union of Sets Example: Let A = { 1, 2, 3, 5, 6, 8, 13 } and B = { 1, 3, 4, 6, 7, 11 }. Give the union of A and B.

Union of Sets: Venn Diagrams Example: Let A = { 1, 2, 3, 5, 6, 8, 13 } and B = { 1, 3, 4, 6, 7, 11 }. Give the union of A and B A U B is the entire region Shade this area.

Empty Set or Null Set Empty set or null set is a set that contains no members. Represented as { } or ø Can you think of an example?

Empty Set or Null Set Empty set or null set is a set that contains no members. Example: Let S = the set of even integers, and T = the set of odd integers. Find S ∩ T. No integer is both odd and even, so: S ∩ T = { }

Activity Find a partner. 1.Write down your full name. 2.Make one set for each person. 3.Label each set using a letter to represent that person. 4.Include all the letters in your name in your set (Remember: each letter should only appear once). 5.Find both the intersection and union for the two sets. 6.Write the intersection and union using braces and using a Venn Diagram.

Graphs of Intersections and Unions Graph the set of all numbers s such that s > -2 or s < -10. The word or means that you need to find the union.

Example The label on a paint can says, “For best results, do not use if the temperature is above 90° or below 50°.” a.Use an inequality to describe each interval in which you should not paint. b.Graph the temperature in which you should not paint. Then graph the recommended temperatures for painting, and describe them with an inequality. a.What temperatures are recommended for painting?

Follow Up Work with a partner or by yourself to complete 1-15 odd on pages Begin homework. Work with a partner or by yourself to complete 1-15 odd on pages Begin homework.