WOODBROOK SECONDARY SCHOOL MATHEMATICS SET THEORY FORM 4 1 | Page Definition of a Set A set is a collection of well defined objects. Capital letters are used to denote a set and set brackets {} are used to list the objects that can be found in that set. Building a Set A set must be defined. Ex. Let A be the set of the first 5 even numbers. Next find the objects that belong to this set. Ex. 2, 4, 6 ,8 ,10 State the set. Ex. A = {2, 4, 6, 8, 10} Common Sets The set of natural numbers or counting numbers: N = {1, 2, 3, 4, 5, …..} The set of whole numbers: W = {0, 1, 2, 3, 4, 5, …..} The set of integers: Z = {….., -3, -2, -1, 0, 1, 2, 3,…..} 1. Let M be the set of the first 7 prime numbers. Using set notation, state the set M. M = { } Even numbers are numbers that can be divided by 2 without leaving a remainder. There are 5 objects in ascending order in this set and all the objects are divisible by 2 A prime number is a number that can be divided by 1 and itself.
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WOODBROOK SECONDARY SCHOOL
MATHEMATICS
SET THEORY
FORM 4
1 | P a g e
Definition of a Set
A set is a collection of well defined objects.
Capital letters are used to denote a set and set brackets {} are used to list the objects that can be
found in that set.
Building a Set
A set must be defined.
Ex. Let A be the set of the first 5 even numbers.
Next find the objects that belong to this set.
Ex. 2, 4, 6 ,8 ,10
State the set.
Ex. A = {2, 4, 6, 8, 10}
Common Sets
The set of natural numbers or counting numbers: N = {1, 2, 3, 4, 5, …..}
The set of whole numbers: W = {0, 1, 2, 3, 4, 5, …..}
The set of integers: Z = {….., -3, -2, -1, 0, 1, 2, 3,…..}
1. Let M be the set of the first 7 prime numbers. Using set notation, state the set M.
M = { }
Even numbers are
numbers that can be
divided by 2 without
leaving a remainder.
There are 5 objects in
ascending order in this
set and all the objects
are divisible by 2
A prime number is a
number that can be
divided by 1 and itself.
WOODBROOK SECONDARY SCHOOL
MATHEMATICS
SET THEORY
FORM 4
2 | P a g e
2. Let P be the set of 5 common flavours of ice-cream. Using set notation, state the set P.
P = { }
3. Let K be the set of 5 popular brands of cars in Trinidad. Using set notation, state the set
K.
K={ }
4. Let G be the set of the first 10 odd numbers.
Using set notation, state the set G.
G = { }
Belonging to a Set
An object that belongs to a set can be represented using the symbol ‘∈’ otherwise if it does not
belong to the set, the symbol ‘∉’ is used.
Let A be defined as follows: A = {2, 4, 6, 8, 10}
Determine which of the numbers from 1 through 10 belongs to the set A.
By inspection,
2 ∈A,
4 ∈A,
6 ∈A,
8 ∈A,
10 ∈A
1∉A
3 ∉A
5 ∉A
7 ∉A
9 ∉A
An odd number is a
number that leaves a
remainder of 1 when
divided by 2
These elements
can be found in A
These elements cannot
be found in A
WOODBROOK SECONDARY SCHOOL
MATHEMATICS
SET THEORY
FORM 4
3 | P a g e
The Empty or Null Set
Consider an empty school bag or an empty wallet or an empty room. If one was to look for a
book or money or a person respectively, nothing will be found.
The empty set, therefore, is the set that contains no objects and is given the set symbol, {∅}.
N.B. The empty set is a subset of all sets.
Let A be the set of pigs that fly. Using set notation, state the objects that belong to A.
Since there are no pigs that fly, A = {∅}.
Let D be the set of all dragons that could fly. Using set notation, state the objects that belong to
D.
Since there are no dragons that fly, D = {∅}.
Finite Set
A finite set is a set where there is a constriction on the number of objects that can be placed in a
set.
Ex. Let B be the set of the first 4 multiples of 5.