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2.3 Set Operations Objectives:

2.3 Set Operations Objectives:. Be able to p erform the set operations of union, intersection, complement, and difference Understand the order in which to perform set operations Know how to apply DeMorgan’s laws in set theory Use Venn diagrams to prove or disprove set theory statements

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2.3 Set Operations Objectives:

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  1. 2.3 Set Operations Objectives: • Be able to perform the set operations of union, intersection, complement, and difference • Understand the order in which to perform set operations • Know how to apply DeMorgan’s laws in set theory • Use Venn diagrams to prove or disprove set theory statements • Calculate the cardinal number of the union of two sets

  2. Union of Sets

  3. Union of Sets cont. • Example: Find the union of the two sets. • Find the union of the two sets. • A = { x : x is the opposite of a natural number } • B = { x : x is a whole number } ____________________________________________ ?

  4. Intersection of Sets

  5. Intersection of Sets cont. • Example: Find the intersection of the two sets. • Find the intersection of the two sets. • A = { x : x is the opposite of a natural number } • B = { x : x is a whole number } ____________________________________________ ?

  6. Set Complement Note: Think of A complement as not A .

  7. Set Complement cont. • Example: Given U and A, find the complement of A. • Given U and A, find the complement of A. • U = { x : x is a real number } • A = { x : x > 3.1 } • A’ = _________________________________ ?

  8. Set Difference B - A Note 1: Think of B – A as what is in B “take away” what is in A . Note 2: B – A A – B !

  9. Set Difference cont. • Example: Find the difference. • Find the differences. • A = { x : x is an integer } • B = { x : x is a natural number } • A – B = ________________________________ ? • B – A = ________________________________ ?

  10. Order of Set Operations • Similar to Order of Operations for arithmetic. • Example: Let

  11. Order of Set Operations cont. • Similar to Distributive Property of Multiplication over Addition. a( b + c ) = ________________________ ? • Intersection distributes over union. • Use Venn diagrams to show

  12. DeMorgan’s Laws Use Venn diagrams to prove DeMorgan’s Laws for sets.

  13. Cardinality of a Union Let A = { 1, 2, 3 } and B = { 3, 4, 5 } Then _________________________ ? and n( ) = _________ ? n ( ) =

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