Union & Intersection of Sets Second Quarter Lesson.pptx

PPT

1. MATATAG 7 Grade Union & Intersection Part 3 of 3 Sets of

2. evaluate basic set operations, including union and intersection of sets visualize and use the Venn Diagram to illustrate and compare sets OBJECTIVES

3. Union and Intersection of Sets

4. Union of Sets The union of sets A and B, denoted by A ⋃ B, is the set containing all elements that are in A, or in B, or in both A and B. Venn Diagram Example: A = {2, 3, 4, 5} B = {3, 5, 6} A ⋃ B = {2, 3, 4, 5, 6} 2 4 6 3 5 A B

5. Intersection of Sets The intersection of sets A and B, denoted by A ⋂ B, is the set containing all elements that are in both A and B. Venn Diagram Example: A = {1, 3, 4, 6, 8} B = {2, 3, 4, 6, 10} A ⋂ B = {3, 4, 6} 1 8 2 3 6 A B 4 10

6. Union and Intersection of Sets ⋂ The word "or" suggests union while the word "and" means intersection. "or" ⋃ nion i tersection "and"

7. EXAMPLES: 1. Let M = {b, e, a, u, t, y} and N = {b, r, a, i , n}. What is M ⋃ N? What is M ⋂ N? Illustrate using a Venn Diagram. M = {b, e, a, u, t, y} N = {b, r, a, i , n} M ⋃ N = {b, e, a, u, t, y, r, i , n} M b N a e u t y r i n M ⋂ N = {b, a} M b N a e u t y r i n Union and Intersection of Sets

8. EXAMPLES: 2. Let O = {positive odd numbers} and E = {positive even numbers}. What is the union of sets O and E? What is O ⋂ E? O ⋃ E = {1, 2, 3, 4, 5, …}. O ⋂ E = { } or Ø Union and Intersection of Sets O = {1, 3, 5, 7, …} E = {2, 4, 6, 8, …}

9. EXAMPLES: 3. If R = {positive even numbers less than 24} and S = {factors of 24}, then what is R ⋂ S? What is the cardinality of R ⋂ S? R ⋂ S = {2, 4, 6, 8, 12} cardinality is 5 Union and Intersection of Sets R = {2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22} S = {1, 2, 3, 4, 6, 8, 12, 24} factors of 24: 1 x 24 2 x 12 3 x 8 4 x 6

10. Exercise Given the sets below. Evaluate and illustrate the following union and intersections using the Venn Diagram U = {0, 1, 2, 3, 4, 5} A = {0, 1, 2} B = {1, 3, 5} C = {3, 4} D = {3} 1) A ⋃ B 2) C ⋃ D 3) A ⋂ C 1. A ⋃ B = {0, 1, 2, 3, 5} 2. C ⋃ D = {3, 4} 3. A ⋂ C = { } A B 1 2 5 3 C D 3 4 U 4 U 1 2 5 A C 1 U 3 2 5 4 4) B ⋂ D

11. Exercise Given the sets below. Evaluate and illustrate the following union and intersections using the Venn Diagram U = {0, 1, 2, 3, 4, 5} A = {0, 1, 2} B = {1, 3, 5} C = {3, 4} D = {3} 4. B ⋂ D = {3} (A ⋃ C) ⋂ (B ⋃ D) B D 3 1 5 U 4 2 Evaluate (A ⋃ C) ⋂ (B ⋃ D) ={1, 3} {0, 1, 2, 3, 4} ⋂ {1, 3, 5} 1) A ⋃ B 2) C ⋃ D 3) A ⋂ C 4) B ⋂ D

12. Thank You for Listening