Introduction for learning solution set:
Theory:
Set is an achievement of our recent mathematics. It appears in all branches. It originated when mathematicians attempted to axiomatize mathematics within the frame work of logic. Mathematicians developed the theory of sets and solutions of set. It becomes a milestone in the growth of mathematics. Now we proceed to introduce the concept of a set. We are learning the solution of set by operations. Let us see about learning solution set in this article. Please express your views of this topic Union Set Theory by commenting on blog.
Learning Solution Set : Set Operations
We shall now study about the set operations
(i) Union of two sets
(ii) Intersection of two sets
(iii) complements
(i) Union of two sets
Let A and B be two given sets. The set of all elements that belong either to A to either to B or to A or to both is called the union of A and B. We denote the union of A and B by A U B. We are learning the union by following expression:
A U B = { x | x ∈ A or x ∈ B or x ∈ A and B}.
We write A U B = {x| x ∈ A or x ∈ B} where it is understood that the word or is used in the inclusive sense; that is, x ∈ A or x ∈ B stands for x ∈ A or x ∈ B or x ∈ A and B.
(ii) Intersection of two sets
Let A and B be two given sets. The set formed by the elements that are common to both A and B is called the intersection of A and B. We denote the intersection of A and B by A ∩B. We are learning intersection by following expression:
A ∩ B = {x | x ∈ A and x ∈ B}.
(iii) Complements:
Subtract the given sets A and B. Learning solution by A - B.
Is this topic Less than Greater than hard for you? Watch out for my coming posts.
Learning Example Solutions for Set Operations:
Find the solution for following examples:
1). If A = {1, 2, 3, 4} and B = {3,4, 6}, find A UB.
Solution:
List the elements of both A and B and avoid duplication.
Thus, A UB = {1, 2, 3, 4, 6}.
2). If A = {4,5,6,7} and B = {5,6,8}, find A∩B.
Solution:
All elements in A and B: 4,5,6,7,5,6,8.
Common elements in A and B:5,6
∴ A ∩B = {5,6}.
3). If A = {2,3,4,5}, B={3,4,5}, find A - B.
A - B = {2}.
Theory:
Set is an achievement of our recent mathematics. It appears in all branches. It originated when mathematicians attempted to axiomatize mathematics within the frame work of logic. Mathematicians developed the theory of sets and solutions of set. It becomes a milestone in the growth of mathematics. Now we proceed to introduce the concept of a set. We are learning the solution of set by operations. Let us see about learning solution set in this article. Please express your views of this topic Union Set Theory by commenting on blog.
Learning Solution Set : Set Operations
We shall now study about the set operations
(i) Union of two sets
(ii) Intersection of two sets
(iii) complements
(i) Union of two sets
Let A and B be two given sets. The set of all elements that belong either to A to either to B or to A or to both is called the union of A and B. We denote the union of A and B by A U B. We are learning the union by following expression:
A U B = { x | x ∈ A or x ∈ B or x ∈ A and B}.
We write A U B = {x| x ∈ A or x ∈ B} where it is understood that the word or is used in the inclusive sense; that is, x ∈ A or x ∈ B stands for x ∈ A or x ∈ B or x ∈ A and B.
(ii) Intersection of two sets
Let A and B be two given sets. The set formed by the elements that are common to both A and B is called the intersection of A and B. We denote the intersection of A and B by A ∩B. We are learning intersection by following expression:
A ∩ B = {x | x ∈ A and x ∈ B}.
(iii) Complements:
Subtract the given sets A and B. Learning solution by A - B.
Is this topic Less than Greater than hard for you? Watch out for my coming posts.
Learning Example Solutions for Set Operations:
Find the solution for following examples:
1). If A = {1, 2, 3, 4} and B = {3,4, 6}, find A UB.
Solution:
List the elements of both A and B and avoid duplication.
Thus, A UB = {1, 2, 3, 4, 6}.
2). If A = {4,5,6,7} and B = {5,6,8}, find A∩B.
Solution:
All elements in A and B: 4,5,6,7,5,6,8.
Common elements in A and B:5,6
∴ A ∩B = {5,6}.
3). If A = {2,3,4,5}, B={3,4,5}, find A - B.
A - B = {2}.
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