01 - INTRODUCTION TO SETS newG7 powerpoint.pptx

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1. INTRODUCTION TO SETS

2. 11 . It is well-defined collection of objects with the same characteristics. Cardinality B. Elements Members D . Sets

3. 4. Which of the following is a well-defined set? A. Cardinality B. Elements Members D . Sets

4. ODD OUT! Face masks Gloves Googles Umbrella

5. ODD OUT! Alcohol Disinfecting solution Face powder Hand Sanitizer

6. ODD OUT! Doctor Nurse Police Student

7. NAME IT! SET OF FRUITS

8. SET OF MUSICAL INSTRUMENTS NAME IT!

9. SET OF SHAPES NAME IT!

10. NAME IT! SET OF PLANETS SET OF HEAVENLY BODIES

11. NAME IT! SET OF NUMBERS

12. WHAT IS A SET? A set is defined as collection of well-defined objects called elements that share common characteristic.

13. HOW DO WE WRITE A SET? In writing a set, we use a CAPITAL LETTER. The elements of a set are written inside a pair of curly braces “ { } ”. Example: S = { 1, 2, 3, 4, 5 }

14. TAKE NOTE:  

15. EXAMPLES:    

16. WELL-DEFINED SET A set is considered as well-defined if and only if a given element is included in the set.

17. EXAMPLES OF WELL-DEFINED SETS Set of prime numbers less than 20 Set of rainbow colors Set of days in a week Set of Philippine Presidents Set of quadrilaterals

18. EXAMPLES OF NOT WELL-DEFINED SETS Set of honest students Set of popular actors Set of successful people Set of best songs of 2020 Set of delicious foods

19. TWO WAYS OF DEFINING A SET There are two ways of defining a set. These ways are Roster Method and Rule Method .

20. ROSTER/LISTING METHOD The elements of the set are listed, separated by commas, and enclosed within a pair of braces.

21. EXAMPLES #1 & #2: Set of first 5 multiples of 3 M = { 3, 6, 9, 12, 15 } Set of first 8 prime numbers Z = { 2, 3, 5, 7, 11, 13, 17, 19 }

22. 6. A = { x│x is a day in a week}

23. 7 . The set of DSWD SAP financial assistance recipients

24. 8. B = {red, blue, yellow}

25. 9 . C = { x│x is a town in NCR with less 10 number of people infected by COVID-19}

26. 10. The set of even numbers less than 10.

27. EXAMPLES #3 & #4: Set of rainbow colors R = { red, orange, yellow, green, blue, indigo, violet } Set of vowels V = { a, e, i, o, u }

28. EXAMPLE #5: Set of Grade 7 subjects T = { Filipino, English, Math, Science, AP, EsP, TLE, MAPEH }

29. RULE METHOD/SET-BUILDER NOTATION We may indicate a set by enclosing in braces a descriptive phrase.

30. EXAMPLE #1: H = { square, rectangle, rhombus, parallelogram, kite, trapezoid } H = { x | x is a set of quadrilaterals } or { x | x is a set of four-sided polygons }

31. EXAMPLE #2: N = { 2, 4, 6, 8, 10 } N = { x | x is a set of first 5 even numbers } or { x | x is a set of even numbers less than 11 }

32. EXAMPLE #3: H = { Jollibee, McDonald, KFC, Greenwich, Chowking } H = { x | x is a set of fast food restaurants }

33. EXAMPLE #4: W = { Iphone, Oppo, Samsung, Vivo, Huawei } W = { x | x is a set of cellphone brands }

34. EXAMPLE #5: G = { 4, 6, 8, 9, 10 } G = { x | x is a set of first 5 composite numbers } or { x | x is a set of composite numbers less than 11 }

35. WHAT IS A SUBSET? A set X is a subset of set Y if all the elements of set X are also the elements of set Y. In symbols, we write it as X ⸦ Y .

36. EXAMPLE: X = { 2, 3, 9 } Y = { 1, 2, 3, 4, 5, 7, 9 } Is it X ⸦ Y or Y ⸦ X ?

37. PROPER SUBSET Set X is a proper subset of set Y if set X does not contain all the elements of Y.

38. EXAMPLE: If X = { 2, 3, 9 } Y = { 1, 2, 3, 4, 5, 7, 9 } , then X is a proper subset of Y (X ⸦ Y).

39. IMPROPER SUBSET Set X is an improper subset of set Y if the elements of X are also the elements of Y.

40. EXAMPLE: If X = { 2, 3, 6, 9 } Y = { 3, 9, 2, 6 } , then X is an improper subset of Y ( X ⸦ Y).

41. UNIVERSAL SET A universal set is a set that contains all the elements under consideration. The symbol for universal set is U .

42. EMPTY OR NULL SET  

43. EXAMPLES: P = {Set of two-legged dog breeds. Q = Set of 3-sided squares. R = Set of odd numbers divisible by 2. S = Set of dinosaurs living on Earth.

44. CARDINALITY OF A SET The cardinality of a set refers to the total number of elements in a set. We use n(A) to denote the cardinality of set A.>

45. EXAMPLES: If P ={ { 2, 3, 6 }, then n(P) = 3. If M ={ { d, e, f, g, h, i }, then n(M) = 6. What is the cardinality of the word “mathematics”? Answer is 8.

46. NUMBER OF SUBSETS IN A GIVEN SET  

47. EXAMPLE #1:  

48. EXAMPLE #1.1: List down the subsets of set A ={ { 5, 6, 7 } . A ={ { 5 } { 6 } { 7 } { 5, 6 } { 5, 7 } { 6, 7 } { 5, 6, 7 } Ø

49. EXAMPLE #2: List down the subsets of R = { l, o, v, e }. What is number of elements? 4 What is the total number of subsets of set R?  

50. EXAMPLE #2.1: List down the subsets of set R ={ { l, o, v, e } . A ={ { l } { o } { v } { l, o } { l, v } { l, e } { o, e } { v, e } { l, o, v } { e } { o, v } { l, o, e } { l, v, e } { o, v, e } { l, o, v, e } {} or Ø

51. KINDS OF SETS

52. FINITE SET It is a set with the limited number of elements.

53. INFINITE SET It is a set with un limited number of elements. The ellipsis (…) is used to denote an infinite set.

54. EMPTY or NULL SET It is a set with no elements. It is denoted by or .  

55. Sets may come in pairs.

56. EQUAL SETS Sets with exactly the same elements (not necessarily in the same order)

57. EQUIVALENT SETS Sets with the same number of elements.

58. JOINT SETS Sets with common elements.

59. DISJOINT SETS Sets with NO common elements.