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Objective- To use intersection and union to simplify problems involving sets.

Objective- To use intersection and union to simplify problems involving sets. Operations with Sets. A = { 1, 2, 3 ,4, 5}. B = { 2, 4, 6, 8, 10}. C = { 5, 6, 7, 8}. ( and ). Intersection ( ). - the elements which are common to both sets. { 2, 4}. 1) A B =.

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Objective- To use intersection and union to simplify problems involving sets.

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  1. Objective- To use intersection and union to simplify problems involving sets. Operations with Sets A = { 1, 2, 3 ,4, 5} B = { 2, 4, 6, 8, 10} C = { 5, 6, 7, 8} ( and ) Intersection ( ) - the elements which are common to both sets. { 2, 4} 1) A B = 4) (A B) C { 2, 4} { 5, 6, 7, 8} { 6, 8} 2) B C = { } or “empty set” { 5 } 3) A C = or “null set” or O

  2. Operations with Sets A = { 1, 2, 3 ,4, 5} B = { 2, 4, 6, 8, 10} C = { 5, 6, 7, 8} - the combined set of elements from two sets with no duplication of elements. Union ( ) ( or ) { 1, 2, 3, 4, 5, 6, 8, 10} 1) A B = { 2, 4, 5, 6, 7, 8, 10} 2) B C = { 1, 2, 3, 4, 5, 6, 7, 8} 3) A C =

  3. A = { 1, 2, 3 ,4, 5} B = { 2, 4, 6, 8, 10} C = { 5, 6, 7, 8} Draw Venn Diagrams to represent... 1) A B 2) A B A B 2 1 6 3 8 4 5 10

  4. A = { 1, 2, 3 ,4, 5} B = { 2, 4, 6, 8, 10} C = { 5, 6, 7, 8} Draw Venn Diagrams to represent... 1) A B 2) A B A B A B 2 2 1 6 3 1 6 3 8 8 4 4 5 10 5 10

  5. A = { 1, 2, 3 ,4, 5} B = { 2, 4, 6, 8, 10} C = { 5, 6, 7, 8} Draw Venn Diagrams to represent... 1) A B 2) A B A B A B 2 2 1 6 3 1 6 3 8 8 4 4 5 10 5 10 Note: The only difference is the shading.

  6. Number Line Graphs of Inequalities Intersections Unions x < 5 x < 3 x < 5 x < 3 0 1 2 3 4 5 6 0 1 2 3 4 5 6 { x : x < 3 } { x : x < 5 } x < 5 x > 3 x < 5 x > 3 0 1 2 3 4 5 6 0 1 2 3 4 5 6 { x : 3 < x < 5 } { x : x = Any Real Number }

  7. Number Line Graphs of Inequalities Intersections Unions x > 5 x < 3 x > 5 x < 3 0 1 2 3 4 5 6 0 1 2 3 4 5 6 { } { x : x < 3 or x > 5 } x > 5 x > 3 x > 5 x > 3 0 1 2 3 4 5 6 0 1 2 3 4 5 6 { x : x > 5 } { x : x > 3 }

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