Q1_1SETS GRADE 7 MATHEMATICS LESSON.pptx

LESSON ON MATH 7 SETS

1. SCHOOLS DIVISION OF BAYAWAN CITY THE WONDERS OF SETS

2. Sets are named by any capital letter. Each object in a set is called element of the set and is denoted by the symbol The statement blue is an element of A can also be written as “blue A” Elements can only be written once and are enclosed by braces and are separated by commas.   DEFINITION OF SETS

3. Group of objects are said to be well defined if anyone agrees that an object belongs to a group otherwise it is not well defined . 1.1. WELL DEFINED AND NOT WELL DEFINED SETS

4. Example of well defined sets. The vowels in the English alphabet. The months of a year Even numbers from 0 to 10. WELL DEFINED AND NOT WELL DEFINED SETS Example of not well defined sets. Group of intelligent students List of beautiful students in your school. A basket of different delicious fruits

5. A set is a finite set if all of its elements of the set can be listed down. 1.2. FINITE, INFINITE AND NULL SETS Examples of finite sets. Set A is the set of days in a week. Set B is the set of natural numbers between 5 and 12  

6. A set is an infinite set if not all of its elements of the set can be listed down. FINITE, INFINITE AND NULL SETS Examples of infinite sets. Set C is the set of natural numbers. Set D is the set of prime numbers. Note: An ellipses (…) is the three dots which indicates that the series of elements are continuous.  

7. Null set or Empty set is the set containing no elements and is denoted by or   FINITE, INFINITE AND NULL SETS Examples of empty or null sets. Set E is the set of whole number less than zero. or Set F is the set of cars with two wheels.  

8. Power set is a set which includes all the subsets including the empty set and the original set itself. It is usually denoted by P. OTHER KINDS OF SETS Example of Power Set Let us say Set A = { a, b, c } Number of elements: 3 Therefore, the subsets of the set are: { } which is the null or the empty set { a } { b } { c } { a, b } { b, c } { c, a } { a, b, c }

9. Example of Power Set Let us say Set A = { a, b, c } Number of elements: 3 Therefore, the subsets of the set are: { } which is the null or the empty set { a } { b } { c } { a, b } { b, c } { c, a } { a, b, c } The power set P(A) = { { } , { a }, { b }, { c }, { a, b }, { b, c }, { c, a }, { a, b, c } } Now, the Power Set has 2 3  = 8 elements.

10. OTHER KINDS OF SETS Equal set. Two sets are equal if an only if they contain exactly the same elements. Equivalent set. Two sets are equivalent if and only if there is a one-to-one correspondence between the sets.

11. OTHER KINDS OF SETS Equal set. The set with no elements. Also called the null set . Denoted by the symbol f. E xample: The set of real numbers x that satisfy the equation

12. UNIVERSAL SETS AND SUBSETS Universal set. It is denoted by U, contains all elements being considered in a situation. Subset Set A is a subset of B, written as “A B” if and only if every element of a is also in B   Proper Subset Set A is a proper subset of B, written as “A B” if and only if every element of a is also in B and that B contains at least one element that is not in A.  

13. Cardinality of set A denoted by n(A) refers to the number of elements in a given set. CARDINALITY OF SET Examples. n(A) = 5 Set M is the set of the months in a year. n(M) = 12  

14. VERBAL DESCRIPTION METHOD It is a method of describing sets in form of a sentence. 1.3. WAYS OF DESCRIBING SET Examples.  

15. ROSTER/LISTING METHOD This method of describing sets in done by listing each elements inside braces and each element are separated by commas 1.3. WAYS OF DESCRIBING SET Examples.  

16. SET BUILDER OR RULE METHOD It is a method that list the rules that determines whether n object is an element of the set rather than the actual elements 1.3. WAYS OF DESCRIBING SET Examples.  

17. QUIZ TIME

18. SCHOOLS DIVISION OF BAYAWAN CITY OPERATIONS SET MODULE 1

19. Unions The union of two sets A and B is The word “or” is inclusive.

20. Intersections The intersection of A and B is Example : Let A be the set of even positive integers and B the set of prime positive integers. Then Definition : A and B are disjoint if

21. Complements If A is a subset of the universal set U , then the complement of A is the set Note: ;

22. Venn Diagrams A Set A represented as a disk inside a rectangular region representing U. U

23. Possible Venn Diagrams for Two Sets U A B U A B U A B

24. The Complement of a Set A The shaded region represents the complement of the set A A c

25. The Union of Two Sets U A B

26. The Intersection of Two Sets U A B

27. Sets Formed by Two Sets R 1 R 3 U A B R 2 R 4

28. Two Basic Counting Rules If A and B are finite sets, 1. 2. See the preceding Venn diagram.

29. INTERSECTION OF SETS The intersection of sets A and B is the set containing the elements that are common to both A and B.   OPERATION ON SETS Examples. Consider set A

30. YOU AND GOD BLESS 😙😁😊 THANK US ALL