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.

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 = { xΙx is an even number }
D = { yΙy 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 Ø .
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 = { xΙx is a multiple of 4 }
D = { yΙy is a student in grade 7 }