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3.8 Subsets ( )

Some or ALL Elements of a given set. Ex : U { Natural numbers }. 3.8 Subsets ( ). →U = { 1,2,3,….}. A { x | 0 < x ≤ 9 }. →A = { 1,2,3,4,5,6,7,8,9}. We say that A is a subset of U and we write it as: A U.

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3.8 Subsets ( )

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  1. Some or ALL Elements of a given set Ex:U { Natural numbers } 3.8 Subsets ( ) →U = { 1,2,3,….} A { x | 0 < x ≤ 9 } →A = { 1,2,3,4,5,6,7,8,9} We say that A is a subset of U and we write it as: A U

  2. : The UNION of two or more sets is the set that contains ALL the elements of the sets →U = { 1,2,3,…∞} Ex: U { Natural numbers } A { x | 0 < x ≤ 9 } B { x | 0 < 2x < 12} Union (U) →A = { 1,2,3,4,5,6,7,8,9} →B = { 2,4,6,8,10} VENN DIAGRAM A U B = 1, 2, 3, 4, 5, 6, 7, 8, 9 2, 4, 6, 8,10 NOTICE: we must never repeat elements in a union of sets, So what do we DO?

  3. 1, 2, 3, 4, 5, 6, 7, 8, 9 2, 4, 6, 8, 10 Union (U) A U B = { 1,2,3,4,5,6,7,8,9,10}

  4. The INSTERSECTION of two or mores sets is the set of elements that are COMMON to every set. ( elements that belong to ALL the sets) INTERSECTION (∩) Ex:U { Natural numbers } A { x | 0 < x < 9 } B { x | 0< 2x < 9}

  5. Ex: U { Whole numbers } A { x | 0 ≤ x ≤ 9 } B { x | 0 < 2x < 13} →A = { 0,1,2,3,4,5,6,7,8,9} →B = { 2,4,6,8,10,12} INTERSECTION (∩) 2, 4, 6, 8 0, 1, 3, 5, 7, 9 10, 12 Thus A ∩ B = { 2, 4, 6, 8 } COMPLEMENT: (Elements not in A ∩B) (A ∩ B ) ‘ = { 0, 1, 3, 5, 7, 9, 10, 12}

  6. Ex: U { Whole numbers } A { x | 0 ≤ x ≤ 9 } B { x | 10 < 2x < 18} →A = { 0,1,2,3,4,5,6,7,8,9} DISJOINT : Sets that have nothing in common. →B = { 12,14,16} 0, 1, 2, 3, 4, 5, 6, 7, 8,9 12, 14,16 Thus A and B are Disjointed

  7. GOAL:

  8. REAL-WORLD: Three friends are going camping. The items in each backpack form a set. What is the intersection of items of the backpacks? Create a Venn Diagram.

  9. flashlight map pan sunglasses water First aid kit map hat pan rope water camera first aid kit hat map water

  10. SOLUTION: First look at what they have in common (intersection): pan flashlight rope sunglasses hat map water first aid kit camera

  11. A = { x | x is one of the five letters in the English alphabet} B = { x | x is a vowelC = { x | x is a letter in the world VEGETABLE} YOU TRY IT: Provide a Venn-Diagram to show the intersection of the three sets.

  12. A = { a, b, c, d, e} B = { a, e} SOLUTION: C = { V, E, G, E, T, A, B, L, E} Furthermore: AB= { a,e} AC= { a,e,b} BC= { a,e}

  13. SOLUTION: First look at what they have in common (intersection): A C g b t d c l v a e B

  14. VIDEOS: Sets Sets: http://www.khanacademy.org/math/probability/independent-dependent-probability/basic_set_operations/v/intersection-and-union-of-sets

  15. CLASSWORK:Page 20-22: Problems: 1, 3, 5, 6, 7, 10, 24 25, 35, 36, 45.

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