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Sets & Operation on Sets

Sets & Operation on Sets. General Notation. Terminology & Notations Set-Membership. Set-Builder Notation. Terminology & Notations Set-Inclusion ( Subsets ). Example (1) List all of the subset of the set A = {1, 2, 3, 4 }. Question: Solution: The set A has the following subsets:

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Sets & Operation on Sets

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  1. Sets & Operation on Sets

  2. General Notation

  3. Terminology & NotationsSet-Membership

  4. Set-Builder Notation

  5. Terminology & NotationsSet-Inclusion ( Subsets)

  6. Example (1)List all of the subset of the set A = {1, 2, 3, 4 } Question: Solution: The set A has the following subsets: The empty set Φ The sets consisting of 1 element: {1}, {2} , {3} , {4} The sets consisting of 2 elements: {1,2}, {1,3} , {1,4} , {2,3} , {2,4} , {3,4} The sets consisting of 3 elements: {1,2,3}, {1,2,4} , {2,3,4} The set A = {1,2,3,4} itself

  7. Finite & Infinite Sets 1. Finite Set: A set B is finite if it has a fixed number of elements. That’s there is a positive integer n, such that: the number of the elements is equal to n Examples: { 1,2,3,4,………….,1000000} 2. Infinite Set: A set B is infinite if for any positive integer n, B has a subset such that the number of the elements of C is equal to n. Examples: {1,2,3,4,………………..} (1,2) [1,2]

  8. The Universal Set The set consisting of all elements under consideration when dealing with a specific situation or problem Example (1): When the discussion involves the ratio of the number of students in this class getting at least a score of 16 in the first exam to those getting no less than a score of 12, then the universal set is the set of all students in the class except those getting a score greater than 12 but less than 16. Example (2): When the discussion involves the percentage of the students in this class getting at least a score of 16 in the first exam, then the universal set is the set of all students in the class.

  9. Venn Diagrams A mean of a visual representation of sets. The universal set Uis represented by a rectangle and a subset of U by a region inside the triangle. U B A

  10. U Examples: A is a proper subset of B. D & E have common elements, but none is the subset of the other A B U E D E∩D

  11. U AUB B A

  12. U A B A∩B

  13. Set Difference B U A A - B

  14. Set Complement A AC

  15. Properties of Set Operations

  16. Disjoint & Intersecting Sets A B Two sets are said to be Disjoint if their intersection is empty (equal to Φ). Two sets are said to be intersecting if their Intersection is not empty ( not equal to Φ). A B

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