Introduction to Sets
The concept of sets is important in all branches of modern mathematics. This concept is used in Physics,Chemistry, all Engineering sciences and even in Medical science now-a-days. The mathematician George Cantor has major contribution in introducing and developing the concept of set.A collection of well-defined distinct objects is called a set.
For example
1) Collection of all positive even integers is a set. 2 is in this set and 1 is not in this set.
2) The collection of all obese persons in any city is not a set, as there is no definite criteria for obesity.
Thus, a set is to be understood as a definite collection.
Example :
1) A deck of 52 playing cards.
2) The names of the days of a week.
3) A set of instruments on a geometry box.
The objects of a set are called its elements or members.
If N represents the set of natural numbers . 1,2,3,4,5 ,6,…
So 1,2,3,… are elements of the set N.
Here as 4 is a member of the set A then we write 4 ∈ A and read as 4 belongs to set A or 4 is in an element of set A.
If 0 is not a member of set A then we write 0 ∉ A and read as 0 does not belong to set A.
Important set in Mathematics
1) Set of natural numbers = N = { 1,2,3,4,5,…}
2) Set of whole numbers = W = { 0,1,2,3,… }
3) Set of integers = Z = {…, -3,-2,-1,0,1,2,3, … }
4) Set of rational numbers = Q = { 2 / 3 , -5 / 7, -10 / -3,…} . The elements of this set is in p/q form.
5) Set of real numbers = R = { all whole numbers, integers, rational and irrational numbers}
6) Set of all positive numbers = Z +
Set Theory
• Sets
• Representation of-Set
• Cardinal Number
• Types of -Set
• Pairs of -Set
• Subset
• Complement-Set
• Union of the-Set
• Intersection-set
• Operations on-Set
• De Morgan's Law
• Venn Diagrams
• Venn-diagrams for set
• Venn-diagrams for different situations
• Problems on Intersection of Two-Set
• Problems on Intersection three-set
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