Discrete Math

• Set theory


  A well defined collection of objects of any kind. Must describe its members and this is usually done in one of two days
• Roster method


  Listing or enclosing the list by a pair of braces {}
• Rule method


  Giving a property with distinguishes members of set from objects in the set
• Sets

  are denoted by capital letters A, B, C....
• Elements of a set

  represent by lower cases letters
• Finite set


  a set is a called finite if it contains a distinct elements otherwise, its infinite
• Proper subset

  let a and b be sets. A ⊂ b iff every element of a is in b but there is a   least one element of b that is not in a.
• PROPER SUBSET

  (⊂)
• Equal sets

    Two sets A and B are equal if and only if every element of A is in B and every element of B is in A and is denoted A = B
• Empty set

    denoted by ϕ, a set w/c contains nothing
• UNIVERSAL set ( U )

    The set of all elements under consideration is called the Universal   Set. The Universal Set is usually denoted by U.
• UNIVERSAL SET

  ( U )

   
• Venn diagram

     A GRAPHICAL REPRESENTATION OF SETS BY REGIONS OF PLANE.
• UNION ( ∪ )

    Let A and B be subsets of a universal set U. The union of sets A and B   is the set of all elements in U that belong to A or to B or to both, and is denoted A ∪ B.
• UNION

  ( ∪ )

   
• Intersection ( ∩ )

    Let A and B subsets of a universal set U. The intersection of sets A and B is the set of all elements in U that belong to both A and B and is denoted A ∩ B.
• INTERSECTION

  ( ∩ ) 
• SET DIFFERENCE

    Let A and B be subsets of a universal set U. The difference of “A and   B” is the set of all elements in U that belong to A but not to B, and is denoted A – B or A \ B.
• COMPLEMENT

    Let A be a subset of universal set U. The complement of A is the set of   all element in U that do not belong to A, and is denoted A ̅, A^′ or A^C.
• UNIVERSAL SET

  
• UNION

  
• INTERSECTION

  
• SET DIFFERENCE

  
• COMPLEMENT