Introduction to Sets
In the early twentieth century, JohnEuler Venn solved the word problems in arithmetic with the help of Venndiagram. This method grew popular as it is easy to understand and simple to calculate. So, Venndiagram is associated with his name.
Types of sets
Empty/Null set
A set which does not contain any element is called an empty set or null set. It is denoted by \(\emptyset\)
empty, and is read as phi. In roster form, \(\emptyset\) it is denoted by { }.
For example:
 The set of the whole number less than zero. Clearly there is no whole number less than zero.
Therefore, it is an empty set.  Let A = {x:2 < x <3, x is a natural number}
Here A is an empty set because there is no natural number between 2 and 3.
Note \(\emptyset\) ≠ { 0 } { 0 } is a set having one element. 
Singleton set
A set which has only one element is called singleton set.
For example:
 A = { x:x neither prime nor composite}
It is a singleton set only containing one element i.e. 1.  Let B = { x:x \(\in\) N and x^{2 }= 4}
It is a singleton set only containing one element i.e. 2, which square is 4.
Finite set
A set which contains a definite number of elements is called a finite set. The empty set is also called a finite set.
For example:
 The set of all color in the rainbow.
 A = { 1, 2, 3, 4, 5, 6, 7, 8, 9, ........................................ 50 }
Infinite set
A set which contains never ending element is called infinite set.
For example:
 Set of all point in the plain.
 Set of all prime number.
 B = { x:x \(\in\) W, x = 2n }
Cardinal number of set
The number of distinct element in a given set A is called the cardinal number of A. It is denoted by n(A).
For example:
 B = { x:x \(\in\) N, x<5}
B = {1,2, 3, 4}
Equivalent set
Two set are called to be equivalent if their cardinal number is same i.e. n(A)=n(B). The symbol for denoting an equivalent set is '\(\leftrightarrow\)'.
For example:
A = {1, 2, 3, 4, 5}
B={a, b, c, d, e }
Therefore, A \(\leftrightarrow\) B.
Equal set
Two set are said to be equal if they contain the same element. Every element of a set A has every element of B and every element of B has every element of A.
For example:
A= { a,e, i,o, u }
B= {u, i, o, a, e}
\(\therefore\) A = B
 n(A∪B∪C) = n(A) + n(B) + n(C)  n(A∩B)  n(C∩A)  n(B∩C) + n(A∩B∩C)
 Maximum value of n(A∩B) ↔ minimum value of n(A∩B)
 Minimum value of n(A∩B) ↔ Maximum value of n(A∩B)
 The cardinality of a set is a positive integer but it is not decimal. So n(A) ≠ 50% because 50% = 0.5
 Total of cardinality shown in Venndiagram must be equal to the cardinality of ∪.

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SetQuestions 
Jan 11, 2017 
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in a survey of 120 students it was found that 17 drink neither tea nor coffee 88 drink tea and 26 drink coffee by drawing a venn diagram find out the number of students who drink both tea and coffeeB 
Jan 10, 2017 
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