1. SETS Sets are lists of items that have specific members. Brackets { } are used to denote a set. The ELEMENTS of the set appear inside the { } brackets and are separated by commas.

2. SETS Sets are lists of items that have specific members. Brackets { } are used to denote a set. The ELEMENTS of the set appear inside the { } brackets and are separated by commas. EXAMPLE :{ 1, 2, 3, 4, 5 }

3. SETS Sets are lists of items that have specific members. Brackets { } are used to denote a set. The ELEMENTS of the set appear inside the { } brackets and are separated by commas. EXAMPLE :{ 1, 2, 3, 4, 5 }Elements are 1,2,3,4,5

4. SETS Sets are lists of items that have specific members. Brackets { } are used to denote a set. The ELEMENTS of the set appear inside the { } brackets and are separated by commas. EXAMPLE :{ 1, 2, 3, 4, 5 }Elements are 1,2,3,4,5 { a, c, e, g }

5. SETS Sets are lists of items that have specific members. Brackets { } are used to denote a set. The ELEMENTS of the set appear inside the { } brackets and are separated by commas. EXAMPLE :{ 1, 2, 3, 4, 5 }Elements are 1,2,3,4,5 { a, c, e, g }Elements are a,c,e,g

6. SETS Sets are lists of items that have specific members. Brackets { } are used to denote a set. The ELEMENTS of the set appear inside the { } brackets and are separated by commas. EXAMPLE :Is ‘A’ an element of the set { W, E, A, R } ?

7. SETS Sets are lists of items that have specific members. Brackets { } are used to denote a set. The ELEMENTS of the set appear inside the { } brackets and are separated by commas. EXAMPLE :Is ‘A’ an element of the set { W, E, A, R } ? YES

8. SETS Sets are lists of items that have specific members. Brackets { } are used to denote a set. The ELEMENTS of the set appear inside the { } brackets and are separated by commas. EXAMPLE :Is ‘A’ an element of the set { W, E, A, R } ? YES Is 4 an element of the set { 1, 3, 5, 7, 9 }

9. SETS Sets are lists of items that have specific members. Brackets { } are used to denote a set. The ELEMENTS of the set appear inside the { } brackets and are separated by commas. EXAMPLE :Is ‘A’ an element of the set { W, E, A, R } ? YES Is 4 an element of the set { 1, 3, 5, 7, 9 } NO

10. Finite and Infinite sets Finite set – a set that has a definite number of members EXAMPLES :{ 1, 2, 5, 8, 10 } { q, w, e, r, t, y }

11. Finite and Infinite sets Finite set – a set that has a definite number of members EXAMPLES :{ 1, 2, 5, 8, 10 } { q, w, e, r, t, y } { 1, 2, 3, 4, …, 15, 16, 17 }

12. Finite and Infinite sets Finite set – a set that has a definite number of members EXAMPLES :{ 1, 2, 5, 8, 10 } { q, w, e, r, t, y } { 1, 2, 3, 4, …, 15, 16, 17 } The dots show that the pattern established in the beginning of the set continues up to the end of the set.

13. Finite and Infinite sets Finite set – a set that has a definite number of members EXAMPLES :{ 1, 2, 5, 8, 10 } { q, w, e, r, t, y } { 1, 2, 3, 4, …, 15, 16, 17 } The dots show that the pattern established in the beginning of the set continues up to the end of the set. So the numbers 5 thru 14 would be elements in this set.

14. Finite and Infinite sets Infinite set – a set that has the … at the beginning or end of the list. This set continues in that pattern before or after the dots for an infinite time. EXAMPLES :{ 2, 4, 6, 8, 10, … } - the even numbers continue to (+) infinity

15. Finite and Infinite sets Infinite set – a set that has the … at the beginning or end of the list. This set continues in that pattern before or after the dots for an infinite time. EXAMPLES :{ 2, 4, 6, 8, 10, … } - the even numbers continue to (+) infinity { …, - 3, - 2, - 1, 0 } - this set starts at (-) infinity and the stops at zero

16. SUBSETS : - are a smaller version of what is contained in an original set

17. SUBSETS : - are a smaller version of what is contained in an original set - a set can be its own subset since the members are all contained in the original set

18. SUBSETS : - are a smaller version of what is contained in an original set - a set can be its own subset since the members are all contained in the original set EXAMPLES :Given the set { m, n, o, p, q, r, s, t, u }, is { m, o, r } a subset of the original set ?

19. SUBSETS : - are a smaller version of what is contained in an original set - a set can be its own subset since the members are all contained in the original set EXAMPLES :Given the set { m, n, o, p, q, r, s, t, u }, is { m, o, r } a subset of the original set ? YES, because m, o and r are all members of the original set

20. SUBSETS : - are a smaller version of what is contained in an original set - a set can be its own subset since the members are all contained in the original set EXAMPLES :Given the set { m, n, o, p, q, r, s, t, u }, is { m, o, r } a subset of the original set ? YES, because m, o and r are all members of the original set Given the set { a, b, c, d, …, q, r, s ) is { s, p, o, r, t } a subset of the original set ?

21. SUBSETS : - are a smaller version of what is contained in an original set - a set can be its own subset since the members are all contained in the original set EXAMPLES :Given the set { m, n, o, p, q, r, s, t, u }, is { m, o, r } a subset of the original set ? YES, because m, o and r are all members of the original set Given the set { a, b, c, d, …, q, r, s ) is { s, p, o, r, t } a subset of the original set ? NO, even though s, p, o, and r are in the original set, t isn’t.

22. SUBSETS : Set Builder notation – described the elements in a set

23. SUBSETS : Set Builder notation – described the elements in a set Inequality symbols are used to describe the elements > or <- elements next to them are NOT in the set ≥ or ≤- elements next to them ARE in the set

24. SUBSETS : Set Builder notation – described the elements in a set Inequality symbols are used to describe the elements > or <- elements next to them are NOT in the set ≥ or ≤- elements next to them ARE in the set EXAMPLE # 1: The set builder is { n / n is an integer and 2 < n < 9 }

25. SUBSETS : Set Builder notation – described the elements in a set Inequality symbols are used to describe the elements > or <- elements next to them are NOT in the set ≥ or ≤- elements next to them ARE in the set EXAMPLE # 1: The set builder is { n / n is an integer and 2 < n < 9 } This describes elements from 2 to 9, but 2 and 9 ARE NOT in the set. They are like edges.

26. SUBSETS : Set Builder notation – described the elements in a set Inequality symbols are used to describe the elements > or <- elements next to them are NOT in the set ≥ or ≤- elements next to them ARE in the set EXAMPLE # 1: The set builder is { n / n is an integer and 2 < n < 9 } This describes elements from 2 to 9, but 2 and 9 ARE NOT in the set. They are like edges. The elements would be { 3, 4, 5, 6, 7, 8 }

27. SUBSETS : Set Builder notation – described the elements in a set Inequality symbols are used to describe the elements > or <- elements next to them are NOT in the set ≥ or ≤- elements next to them ARE in the set EXAMPLE # 2: The set builder is { n / n is an integer and n ≥ 4 }

28. SUBSETS : Set Builder notation – described the elements in a set Inequality symbols are used to describe the elements > or <- elements next to them are NOT in the set ≥ or ≤- elements next to them ARE in the set EXAMPLE # 2: The set builder is { n / n is an integer and n ≥ 4 } This describes elements from 4 to infinity, and in this case 4 IS an element The elements would be { 4, 5, 6, 7, 8, … }

29. SUBSETS : Set Builder notation – described the elements in a set Inequality symbols are used to describe the elements > or <- elements next to them are NOT in the set ≥ or ≤- elements next to them ARE in the set EXAMPLE # 3: The set builder is { n / n is an even integer and 2 < n ≤ 10 }

30. SUBSETS : Set Builder notation – described the elements in a set Inequality symbols are used to describe the elements > or <- elements next to them are NOT in the set ≥ or ≤- elements next to them ARE in the set EXAMPLE # 3: The set builder is { n / n is an even integer and 2 < n ≤ 10 } This describes even integers from 2 to 10… 2 will not be included in the set but we will include 10. The elements would be { 4, 6, 8, 10 }

31. ASSIGNMENT : 1.Open the link and print the drill problems. 2.Check your answers with the solution guide