Set Theory Homework and Assignment Help

One important but complicated part of mathematics is Set Theory that is easy to understand but difficult to solve. Set theory plays an important role in economics, physics, engineering and biology. Set theory is widely used, right from high school to Ph.D. level. Some problems of set theory are so difficult that students do not get the meaning of the questions asked in their set theory homework. So these students feel anxious while facing those problems. Sometimes they interpret another meaning of these questions and fail in their set theory assignment. We bring good news to these students. MyAssignmenthelp.com now provides full support to all these students in their set theory assignment. Our highly qualified maths writers can easily solve the problems as they are experts in set theory homework. With the help of these experts, students can score good marks in their set theory assignments.

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Set theory introduction

We all use some words like ‘collection of books', 'aggregate of the number' etc. It looks similar to the set concept, but it is not the case. A set is a collection of well-defined objects. It means elements of the set must have well-defined characteristics. So the above examples are not considered as an example of sets. What types of books should be collected? Aggregate of which types of numbers? The elements of a set must have some definite characteristic.

Representation of sets

Two methods are used to represent a set. One is roaster method, and another is set builder method.

• A set of whole numbers can be represented as - W = { 0,1,2,3,....}. This is called roster method.
• W = {x: x is a whole number}.. This is called set builder method.

There are different types of sets like

1. a) Finite sets : If the numerical number of members of a set is finite then the set is called finite set. For an example, a set of set of all integers between 1 and 7 is called finite set. S= { 2,3,4,5,6}
2. b) Infinite sets: If the number of elements of a set is infinite then the set is called infinite set. Example: A set of all positive integers. I = {0,1,2,3,4,......}
3. c) Null sets: If a set has no element then it is called null set and it is expressed as {}, A={ x: x ≠ A, x =A }
4. d) Singleton sets: Some sets have only one element and these sets are called singleton sets. Example- B ={1}
5. e) Equal sets: Two sets X and Y are said to be equal, if all members of X belongs to Y and all members of Y belongs to X. This can be expressed as X=Y
6. f) Equivalent sets: Two distinct sets that are finite are considered as equivalent sets if they have equal number of members in them. Example: C = { 5,6,2,9} and D= { 9,0,2,5}. C and D are called equivalent sets as both have equal numbers of elements in them.
7. g) Universal set: It is a set that contains all elements of all the sets that means all sets are subsets of this set. It is denoted by U.

Venn diagram

It is very easy to represent a set or the relation between two sets through a diagram and this diagram is called Venn diagram. Through a Venn diagram, it can be easily shown that two or more sets have equal number of elements or not.

 

In the above picture, the two sets do not share a single element so set A and B are disjoint sets.

Union of two sets A and B is that set that contains all elements of A or B. U is the universal set. Intersection of two sets contains elements that are common to A and B.

Thus, you can see that we explain things so clearly that students find it interesting to solve these problems.

 

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