UNIT 3 & 4

• Inductive - Using specific observations to form a general conclusion
• Deductive - Using a general premise to form a specific conclusion
• PREMISE – is a previous statement or proposition from which another is inferred or follows as a conclusion.
• NOTATION

  • roster method
  • set builder
• The set with no elements is called the - empty set - or the null set and is designated with the symbol

  
• Venn Diagrams - It is frequently very helpful to depict a set in the abstract as the points inside a circle (or any other closed shape).
• subset -

  
• proper subset -

  
• The set A is a subset of the set B if every element of A is an element of B.
• If A is a subset of B and B contains elements which are not in A, then A is a proper subset of B.
• If two sets A and B are equal we write A = B to designate that relationship.
• equality - if B is not a subset of A. We would write A () B.

  
• Operations on Sets

  • UNION
  • INTERSECTION
  • DIFFERENCE
  • COMPLEMENT
  • CARTESIAN PRODUCT
• The union of two sets A and B is the set containing those elements which are elements of A or elements of B.

  
• The intersection of two sets A and B is the set containing those elements which are elements of A and elements of B.

  
• The difference of two sets A and B is a set whose elements are found in set A but NOT in set B.

  
• The complement of set A is denoted by A'.

  
• The Cartesian product of sets is the collection of all ordered pairs obtained by the product of two non-empty sets.
• Kinds of Sets

  • Empty/Null/Void Set
  • Finite Set
  • Infinite set
  • Universal Set