lec 2

• Set is a well-defined collection of distinct object and is denoted by an uppercase letter
• Ways of Describing a Set

  1. ROSTER / TABULAR METHOD
  2. RULE / DESCRIPTIVE METHOD
• ROSTER / TABULAR METHOD is aMethod in which the elements in the given set are listed or enumerated, separated by a comma, inside a pair or braces
• RULE / DESCRIPTIVE METHOD is a Method in which the common characteristics of the elements are defined. This method uses set builder notation
• Type of Sets

  1. Empty, Null, Void Sets
  2. Finite Sets
  3. Infinite Sets
  4. Universal Set
• EMPTY, NULL, VOID SET – set that has no elements
• EMPTY, NULL, VOID SET - denoted by Ø or by a pair of braces with no element inside.
• FINITE SET - a set with a countable number of elements.
• INFINITE SET – a set has uncountable number of element
• UNIVERSAL SET - the totality of all the elements of the sets under consideration, denoted by U.
• Relation between sets

  1. EQUAL SETS
  2. EQUIVALENT SETS
  3. JOINT SETS
  4. DISJOINT SETS
• EQUAL SETS – set with same elements
• EQUIVALENT SETS – set with the same number of elements.
• JOINT SETS - sets with at least one common element
• DISJOINT SETS – sets that have no common element
• PROPER SUBSET - contain at least one common element from the bigger set
• IMPROPER SUBSET - The set itself and null set
• Power Sets - Set containing all the subset of the given set Formula : 𝟐 𝒏 “wherein n is the number of element”
• Operations on Sets

  1. Union of Sets
  2. Intersection of Sets
  3. Difference of Sets
  4. Complement of Sets
• UNION OF SETS - set whose elements are found in A or B or in both.
• UNION OF SETS - This is denoted by A U B
• INTERSECTION OF SETS - set whose elements are common to both sets.
• INTERSECTION OF SETS - This is denoted by A ∩ B
• DIFFERENCE OF SETS - sets whose elements of A which do not belong to B.
• DIFFERENCE OF SETS - We have, A – B.
• COMPLEMENT OF SETS - the set of elements found in the universal set but not in set A.
• COMPLEMENT OF SETS - This is denoted by 𝐴^C