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Set
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A set is a collection of well defined objects. The object in a set are called elements or members of the set.

Symbols
=







Equal to

Not equal to

Is an element of

Is not an element of

{ } or

n(A)





 Null or empty set

Cardinal number of set A (Number of element in set A)

Union

Intersection


Example: "A" is the set of odd numbers less than 10.
A = {1,3,5,7,9}
1,3,5,7 and 9 are the elements or members of set A.
1 A, whereas
2 A

The objects or elements in the set should be unique, there should be no repetition of same objects or elements in a set.
Example: "A" is the set of letters in word "addition".
A = {a,d,d,i,t,i,o,n} is not correct.
A = {a,d,i,t,o,n} is correct.

A set can be written in three different ways:
Rule form or Descriptive form:
Example: B = {boys in room#301}
A = {Whole numbers less than 10}
C = {vowels}
E = {multiples of 7 less than 98}
D = {5th Grade students who got more than 90% in the test}

Roster method or Tabular method or Listing method:
Example: B = {Tim,David,Sid,Ben,Ken,John,James,Russ}
A = {0,1,2,3,4,5,6,7,8,9}
C = {a,e,i,o,u}
E = {7,14,21,28,35,42,...,98}
The three dots indicate that the pattern of multiples of 7 to be continued upto 98.

Set builder form:
Example: A = {x/x N, 2 < x < 12}
Read as: x such that x is an element of natural numbers greater than 2 and less than 12
A = {3,4,5,6,7,8,9,10,11}
Example: A = {x/x N, x is even}
A = {2,4,6,8,....}
Example: A = {x/x W, x < 5}
Read as: x such that x is an element of whole numbers less than and equal to 5
A = {0,1,2,3,4,5}
Example: A = {x/x N, x is multiple of 3 less than 100}
A = {3,6,9,12,...,99}

Kind of sets:

Finite and Infinite set:
If the members or elements of a set can be counted then the set is called finite set.
Example:A = {1,2,3,4,5,...,10000}, B = {b,e,g,o,s,r,t}
If there is no end to the number of members or elements of a set then the set is called infinite set.
Example:A = {1,2,3,4,5,...}, B = {2,4,6,8,...}

Empty set or Null set or Void set:
Any set with no elements or members is called empty set or null set or void set.
Example:A = {multiples of 10 but less than 10}, B = {even number between 22 and 24}

Singleton set:
Any set with one element or member is called singleton set.
Example:A = {0}, B = {odd number between 98 and 100},

Cardinal number of set:
A = {b,e,g,o,s,r,t}, B = {Tim,David,Sid,Ben,Ken,John,James,Russ}
Number of element in set A is 7 therefore the cardinal number of set A is 7 => n(A) = 7
Number of element in set B is 8 therefore the cardinal number of set B is 8 => n(B) = 8

Equivalent and non-equivalent sets:
A = {b,e,g,o,s,r,t}, B = {Tim,David,Sid,Ben,Ken,John,James,Russ}
Consider Set A and Set B, there is no one to one correspondence between the two sets. The cardinal numbers n(A) = 7 and n(B) = 8 are unequal. The two sets are non-equivalent sets.
A = {b,e,g,o,s,r,t}, B = {Tim,David,Sid,Ben,Ken,John,James}
Consider Set A and Set B there is one to one correspondence between the two sets. The cardinal numbers n(A) = 7 and n(B) = 7 are equal. The two sets are equivalent sets.

Equal sets:
A = {b,e,g,o,s,r,t}, B = {e,t,o,r,s,g,b}
Consider Set A and Set B, they have exactly same elements or objects. They are called equal sets.





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