Sets for grade 8.

Some special sets:
· Equivalent sets.
· Non equivalent sets.
· Universal sets.
· Empty set.
· Infinite set.
· Finite set.

Equivalent sets:
If the number of elements in a set are equivalent to another set, then they are called equivalent sets.
Example:
A= {24, 25, 26 , 27}
B = {100, 200, 300, 400}
The sets are equivalent.

Non equivalent sets:
If the number of element in a set are not equal to another set then the sets are called
non equivalent sets.
Example:
X= {24, 25, 26, 27, 28}
Y = {100, 200, 300, 400}
The sets are non equivalent.

Finite:
If we can count the elements of a set we call it a finite set.
Example:
A = {2, 4, 7, 9}
Here A is a finite set.

Infinite sets:
If we start counting the elements of a set and the process does not come to end, then the set is infinite.
Example:
B = {1, 2, 3, 4, 5,…}
B is an infinite set.

Universal sets:
A set having all the elements of all the particular sets under consideration is called universal set.
Example:
If we are discussing the football team of Brazil then the universal set will be the set of all the teams of football.

Empty set:
A set which has no element is called empty set. It is denoted by empty bracket or by the symbol "j".
Example:
A = { }
A is empty set here.

Operations on sets:
· Union set.
· Intersection of sets.
· Difference of two sets.
· Complement of a set.

Union of two sets:
The union of two sets is a set having elements of both the sets. If the sets have identical elements then they are not repeated in the union set. It is denoted by the symbol " U ".
Example:
A = {1, 2, 3, 4}
B = {4, 5, 6}
A È B = {1, 2, 3, 4} U {4, 5, 6}
A È B = {1, 2, 3, 4, 5, 6}

Intersection of sets:
The intersection of two set is a set having the common elements of the both the sets. If the sets do not have same elements then the intersection of the sets will be an empty set. The symbol used for intersection is "n".
Example:
Y = {1, 2, 3, 4, 5, 6, 7, 8}
X = {2, 4, 6, 8, 10, 12}
Y n X = {2, 4, 6, 8}

Difference of two sets:
The difference of two sets is a set in which we write all those members of first set which are not in the other set.
Example:
L = {11, 12, 13, 14, 15, 16, 17, 18}
M = {12, 14, 16, 18}
L - M = {11, 12, 13, 14, 15, 16, 17, 18}- {12, 14, 16, 18}
L - M = {11, 13, 15, 17}

Complement of a set:
The complement of set is simply the difference of a set with universal set. The complement of a set is denoted by the same name with a "dash" on it.
Example:
U = {21, 22, 23, 24, 25, 26}
A= {21, 22, 23}
A' = U - A = {21, 22, 23, 24, 25, 26}-{21, 22, 23}
A' = {24, 25, 26}

Important points:
· The difference of two sets is not commutative, that is
  A - B ? B - A
· The complement of a universal set is an empty set.
· The complement of an empty set is the universal set.
· Union of two set is not empty unless both the sets are empty.

Typical notations used for writing sets(link to set of 7):
1. Tabulation method
2. Descriptive method.

Tabulation method:
In this method we list all the elements of a set in brackets.
Example:
A = {1,2,3,4}
B = {-1,-3,-5,-6…}

Descriptive method:
In this method we state a property about a set which describes all its members.
Example:
Y is a set of integers.
X is set of multiples of two.

Subsets:
If every member of a set is also a member of another set then the first set s called the subset of the other. It is possible that second set has some elements which are not in the first set.
· Proper subset.
· Improper subset.

Proper subset:
If a set is the subset of another set and at least one element of the second element is not the element of the first set. The symbol of proper subset is " Ì "
Example:
A = {2, 3}
B = {2, 3, 4}
A Ì B.

Improper subset:
When number of elements are equal in both sets we call then improper subset. The symbol for improper subset is "Í".
Example:
X = {2, 3, 4}
Y = {2, 3, 4}
X Í Y.

Power set:
It is the set having all the sets as its member which are subsets of a particular set.
Example:
If set A = {1, 2, 3}, then its power set is;
P(A) = {{},{1},{2},{3},{1,2},{1,3},{2,3},{1,2,3}}

 

 

 

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