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SETS

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. SETS. Sets are lists of items that have specific members. Brackets { } are used to denote a set.

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SETS

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  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 : • Open the link and print the drill problems. • Check your answers with the solution guide

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