1. SECTION 2-3 Set Operations and Cartesian Products Slide 2-3-1

2. SET OPERATIONS AND CARTESIAN PRODUCTS Intersection of Sets Union of Sets Difference of Sets Ordered Pairs Cartesian Product of Sets Venn Diagrams De Morgan’s Laws Slide 2-3-2

3. INTERSECTION OF SETS Slide 2-3-3 The intersection of sets A and B, written is the set of elements common to both A and B, or

4. EXAMPLE: INTERSECTION OF SETS Find each intersection. a) b) Solution a) b) Slide 2-3-4

5. UNION OF SETS Slide 2-3-5 The union of sets A and B, written is the set of elements belonging to either of the sets, or Or

6. EXAMPLE: UNION OF SETS Find each union. a) b) Solution a) b) Slide 2-3-6

7. DIFFERENCE OF SETS Slide 2-3-7 The difference of sets A and B, written A – B, is the set of elements belonging to set A and not to set B, or

8. EXAMPLE: DIFFERENCE OF SETS Slide 2-3-8 Let U = {a, b, c, d, e, f, g, h}, A = {a, b, c, e, h}, B = {c, e, g}, and C = {a, c, d, g, e}. Find each set. a) b) Solution a) {a, b, h} b)

9. ORDERED PAIRS Slide 2-3-9 In the ordered pair (a, b), a is called the first component and b is called the second component. In general Two ordered pairs are equal provided that their first components are equal and their second components are equal.

10. CARTESIAN PRODUCT OF SETS Slide 2-3-10 The Cartesian product of sets A and B, written, is

11. EXAMPLE: FINDING CARTESIAN PRODUCTS Slide 2-3-11 Let A = {a, b}, B = {1, 2, 3} Find each set. a) b) Solution a) {(a, 1), (a, 2), (a, 3), (b, 1), (b, 2), (b, 3)} b) {(1, 1), (1, 2), (1, 3), (2, 1), (2, 2), (2, 3), (3, 1), (3, 2), (3, 3)}

12. CARDINAL NUMBER OF A CARTESIAN PRODUCT Slide 2-3-12 If n(A) = a and n(B) = b, then

13. EXAMPLE: FINDING CARDINAL NUMBERS OF CARTESIAN PRODUCTS Slide 2-3-13 If n(A) = 12 and n(B) = 7, then find Solution

14. VENN DIAGRAMS OF SET OPERATIONS Slide 2-3-14 A B U AB U A U AB U

15. EXAMPLE: SHADING VENN DIAGRAMS TO REPRESENT SETS Slide 2-3-15 Draw a Venn Diagram to represent the set Solution AB U

16. EXAMPLE: SHADING VENN DIAGRAMS TO REPRESENT SETS Slide 2-3-16 Draw a Venn Diagram to represent the set Solution A B C U

17. DE MORGAN’S LAWS Slide 2-3-17 For any sets A and B,