lec 2
Cards (27)
- Set is a well-defined collection of distinct object and is denoted by an uppercase letter
- Ways of Describing a Set
- ROSTER / TABULAR METHOD
- 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
- Empty, Null, Void Sets
- Finite Sets
- Infinite Sets
- 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
- EQUAL SETS
- EQUIVALENT SETS
- JOINT SETS
- 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
- Union of Sets
- Intersection of Sets
- Difference of Sets
- 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