Form 4 Chapter 3
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Sets
A set is a collection of objects with common characteristics.
*Identifying elements of a set
1.The objects in a set are known as elements.
2.For example,if A is a set of even numbers,then 2 is an element of set A.
We write 2 ∈ A an 5 ∉ A.
3.The symbol ∈ is used to denote the phrase 'is an element of' or' is a member of'.
*Representing sets using Venn diagrams
1.Sets can be represented using Venn diagrams.
2.A Venn diagram is an enclosed geometrical diagram in the shape of a circle,ellipse,triangle,square or
rectangle.
3.For example,A = {1,2,3,4} can be represented in the Venn diagram below.
1.The objects in a set are known as elements.
2.For example,if A is a set of even numbers,then 2 is an element of set A.
We write 2 ∈ A an 5 ∉ A.
3.The symbol ∈ is used to denote the phrase 'is an element of' or' is a member of'.
*Representing sets using Venn diagrams
1.Sets can be represented using Venn diagrams.
2.A Venn diagram is an enclosed geometrical diagram in the shape of a circle,ellipse,triangle,square or
rectangle.
3.For example,A = {1,2,3,4} can be represented in the Venn diagram below.
4.Notice that there are 4 elements in set A.Set A can also be represented in a Venn diagram as follows.
*Listing elements and stating the number of element in a setWe use the notation n(A) to represent the number of elements in set A.
*Empty sets
1.An empty set is a set with elements.
2.We use { } or to represent empty sets.
3.For example,M = {x : x < 0 and x is a positive integer} is an empty set as M contains no elements.We write M = or M = { }
*Equal set
1.Two sets,A and B are equal if both have the same elements.
2.For example,A = { 1,2,3,4} and B = {2,4,3,1} are equal sets.It is written as A = B.
3.If set M is not equal to set N,then it is denoted as M ≠ N
3.2 Subset,Universal Set and the Complement of a set
*Subsets
1.Element of set A is also an element of set B,then A is a subset of B.
2.if not all the elements of set M are the elements of set N,then M is not the subset of N.The relationship is
written as M ¢ N
*Representing subsets using Venn diagrams
Subsets can be represented using Venn
*Listing elements and stating the number of element in a setWe use the notation n(A) to represent the number of elements in set A.
*Empty sets
1.An empty set is a set with elements.
2.We use { } or to represent empty sets.
3.For example,M = {x : x < 0 and x is a positive integer} is an empty set as M contains no elements.We write M = or M = { }
*Equal set
1.Two sets,A and B are equal if both have the same elements.
2.For example,A = { 1,2,3,4} and B = {2,4,3,1} are equal sets.It is written as A = B.
3.If set M is not equal to set N,then it is denoted as M ≠ N
3.2 Subset,Universal Set and the Complement of a set
*Subsets
1.Element of set A is also an element of set B,then A is a subset of B.
2.if not all the elements of set M are the elements of set N,then M is not the subset of N.The relationship is
written as M ¢ N
*Representing subsets using Venn diagrams
Subsets can be represented using Venn
*Listing the subsets of a specific set
Given that A = {1,2,3}.The possible subsets of A are ,{1},{2},{3},{1,2},{1,3},{2,3} and {1,2,3}.
*Universal set
1.Universal set is a set consisting of all the elements under discussion.
2.the symbol is used to denote a universal set.
3.All the sets under discussion are subsets of the universal set.
*The complement of a set
1.The complement of set A is a set consisting of all the elements in ,which are not the elements of set A
2.The symbol A' denotes the complement of set A.
3.In the Venn,diagram below,the shaded region represents
Given that A = {1,2,3}.The possible subsets of A are ,{1},{2},{3},{1,2},{1,3},{2,3} and {1,2,3}.
*Universal set
1.Universal set is a set consisting of all the elements under discussion.
2.the symbol is used to denote a universal set.
3.All the sets under discussion are subsets of the universal set.
*The complement of a set
1.The complement of set A is a set consisting of all the elements in ,which are not the elements of set A
2.The symbol A' denotes the complement of set A.
3.In the Venn,diagram below,the shaded region represents
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3.3 Operation on Sets
*Intersection of sets
1.Intersection of set A and B is a set of elements which common to both sets A and B.
2.The intersection of set A and B is denoted by A B.
3.The shaded region in Venn diagram represents A B.
*Intersection of sets
1.Intersection of set A and B is a set of elements which common to both sets A and B.
2.The intersection of set A and B is denoted by A B.
3.The shaded region in Venn diagram represents A B.
1.The complement of A ∩ B is a set containing all the elements which are not the elements of set A ∩ B.
This is denoted by (A ∩ B)'.
*Solving problems involving the intersection of sets
We can solve some problems in our daily life by applying the concepts of the intersection of sets.
*Union of sets
1.The union of sets A and B is a set of elements belonging to either of the sets or both.
2.The symbol A B denotes the union of set A and B.
We can solve some problems in our daily life by applying the concepts of the intersection of sets.
*Union of sets
1.The union of sets A and B is a set of elements belonging to either of the sets or both.
2.The symbol A B denotes the union of set A and B.
*The complement of the union of sets
1.The complement of A U B is a set containing all the elements in the universal set, ξ which are not elements
of the set A U B.This is denoted by (A U B)'.
2.The shaded region in Venn diagram represent (A U B)'.
*Solving problems involving the union of sets
Venn diagram is very useful when solving problems involving the union of sets.
*Combined operations on setsWhen combined operations are involved,carry,out the operations in the brackets first.
*Solving problems involving combined operations on sets
Venn diagram is very useful when solving problems involving the union of sets
Venn diagram is very useful when solving problems involving the union of sets.
*Combined operations on setsWhen combined operations are involved,carry,out the operations in the brackets first.
*Solving problems involving combined operations on sets
Venn diagram is very useful when solving problems involving the union of sets
