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Definition of a Set

Joreen Mae Yap
Joreen Mae Yap

This document defines and provides examples of different types of sets including finite and infinite sets, empty and unit sets, equal and equivalent sets, subsets, and Venn diagrams. It explains that a set is a collection of distinct objects and provides examples of sets containing various elements like letters, numbers, and people. It also describes how to determine the number of elements in a set and defines key terms used to describe relationships between sets.

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Are groups or collections of numbers, things, people, places or any other individual pieces of data.
A = { necklace, bracelet, earrings } B = { a, e, i, o, u } C = { xx is an even number } D = { yy is a counting number from 1 to 5 }
Anything that belongs to a set Set A necklace, bracelet, earrings Set B a, e, i, o, u Set C 2, 4, 6, 8, 10, Set D 1, 2, 3, 4, 5
is the number of elements in a set Set A n(3) Set B n(5) Set C infinite Set D n(5)
EMPTY SET OR NULL SET An empty set is a set which has no element and denoted by { } or . UNIT SET A set containing only one element. UNIVERSAL SET A universal set is a set containing all the elements of the sets under discussion and is denoted by U
FINITE SET As set is said to be finite if its either empty or the element can be counted and the counting process must come to an end. INFINITE SET A set is infinite if it is not finite.
VENN DIAGRAM A Venn Diagram is a pictorial representation of the relationship between sets. JOINT SETS Two or more sets are said to be joint sets if there are at least one element common in the given sets. DISJOINT SETS Disjoint sets are two or more sets with no common element.
EQUAL SETS Equal sets are two or more sets having the same elements. Ex. A = { 5, 10, 15, 20, 25 } B = { 5, 10, 15, 20, 25 } EQUIVALENT SETS Equivalent sets are two or more sets with the same cardinality. Ex. C = { 1, 3, 5, 7 } D = { 9, 11, 13, 15 }
Set A is a subset of B, written as A C B if each element of A is contained in B. Ex. A = { 2, 4,6, 8, 10 } B = { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 }
ROSTER OR LISTING Ex. A = { Celyn, Margaux, Ethan, Liam } B = { 0, 6, 12, 18, 24, 30 } RULE METHOD OR SET-BUILDER NOTATION Ex. C = { xx is a multiple of 4 } D = { yy is a student in grade 7 }

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Definition of a Set

  • 1. Are groups or collections of numbers, things, people, places or any other individual pieces of data.
  • 2. A = { necklace, bracelet, earrings } B = { a, e, i, o, u } C = { xx is an even number } D = { yy is a counting number from 1 to 5 }
  • 3. Anything that belongs to a set Set A necklace, bracelet, earrings Set B a, e, i, o, u Set C 2, 4, 6, 8, 10, Set D 1, 2, 3, 4, 5
  • 4. is the number of elements in a set Set A n(3) Set B n(5) Set C infinite Set D n(5)
  • 5. EMPTY SET OR NULL SET An empty set is a set which has no element and denoted by { } or . UNIT SET A set containing only one element. UNIVERSAL SET A universal set is a set containing all the elements of the sets under discussion and is denoted by U
  • 6. FINITE SET As set is said to be finite if its either empty or the element can be counted and the counting process must come to an end. INFINITE SET A set is infinite if it is not finite.
  • 7. VENN DIAGRAM A Venn Diagram is a pictorial representation of the relationship between sets. JOINT SETS Two or more sets are said to be joint sets if there are at least one element common in the given sets. DISJOINT SETS Disjoint sets are two or more sets with no common element.
  • 8. EQUAL SETS Equal sets are two or more sets having the same elements. Ex. A = { 5, 10, 15, 20, 25 } B = { 5, 10, 15, 20, 25 } EQUIVALENT SETS Equivalent sets are two or more sets with the same cardinality. Ex. C = { 1, 3, 5, 7 } D = { 9, 11, 13, 15 }
  • 9. Set A is a subset of B, written as A C B if each element of A is contained in B. Ex. A = { 2, 4,6, 8, 10 } B = { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 }
  • 10. ROSTER OR LISTING Ex. A = { Celyn, Margaux, Ethan, Liam } B = { 0, 6, 12, 18, 24, 30 } RULE METHOD OR SET-BUILDER NOTATION Ex. C = { xx is a multiple of 4 } D = { yy is a student in grade 7 }