This document defines and provides examples of five types of sets: 1. Infinite sets, which cannot be fully listed, like the set of natural numbers. 2. Finite sets, which can be fully counted and listed, like the set of months in a year. 3. The null or empty set, which contains no elements and is denoted by {} or ∅. 4. Equal sets, which have the same elements in any order. 5. Equivalent sets, which have the same number of elements that are not necessarily the same.

1. SetTheory
Types of Sets
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SecondForm
May2018

2. Objectives:
At the end of this PowerPoint presentation, the
students should be able to:
1. Correctly state the names of the five different
types of sets listed in this presentation.
2. Correctly define each set in their own words.
3. Correctly complete all activities in this
presentation.
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4. Infinite Sets
An infinite set is a set in which all its members
CANNOT be listed.
This set is also called a non-well-defined set.
Examples of infinite sets:
Y = {whole numbers}
 X = {integers}
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5. Finite Sets
A finite set is a set in which all its elements CAN
be counted and named.
This set is also called a well-defined set
Examples of a finite set:
 M = {months of the year}
N = {days of the week}
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6. Activity:
Of the sets listed below, write F beside the finite sets and I
beside the in finite sets in space provided.
______ Y = {natural numbers}
______ Z = {sheep in Ireland}
______ A = {laptop brands}
______ B = {car brands}
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7. Null or Empty Set
This set contains no elements and is denoted by
{ } or ∅
Examples of a null or empty set:
The set of students at May Day High with four
legs
The set students at my school who do not wish
to become teachers
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8. Question:
Examine the sets below and determine whether it
is a finite set, an infinite set or a null set:
1) A = {even numbers}
2) B = {people with six legs}
3) C = {2, 3, 5, 7, 11, 13, …}
4) D = {even numbers less than 100}
5) The set of odd numbers that can be divided
exactly by 2.
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9. Equal Sets
Equal sets have the same number of elements and
exactly the same elements. The order in which the
elements are listed does not matter. Equal sets are
also called identical sets.
Example:
If A = {1, 2, 3} and B = {3, 1, 2}
Then A = B
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10. Equivalent Sets
Equivalent sets are sets which have the same
number of elements, but the elements are not
necessarily the same. This is denoted by ↔.
Example:
If P = {a, b, c} and Q = {p, q, r}
Then P ≠ Q however P↔Q
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11. Activity:
1. State three examples of pairs of equal sets.
2. Write down two examples of unequal sets.
3. State one example of a pair of sets which are
equivalent.
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12. Culminating Activity:
Complete the table below with the corresponding information.
Types of sets Definition of Set Example
All its elements CAN be
listed.
Equal sets
This set contains no
elements and is denoted
by {} and ∅.
The set of natural
numbers.
Two sets containing the
same number of elements
that are not necessarily of
the same kind and is
denoted by ↔.
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