Basic Operations On Sets

posted on: 15 Mar, 2012 | updated on: 30 Aug, 2012

One of the main applications of Sets theory is to make the Relations between two sets. For making these relations, certain operations can be performed on the Numbers. We will discuss Some Basic Operations on Sets.
Union: As the word indicates Union means joining or adding together. Union of Two sets means adding together the two sets. Let us consider two sets ‘A’ and ‘B’, then the union of two sets is represented by “A U B”, which means all the elements which either belong to ‘A’ or ‘B’. Here are some examples: If A= 1, 2, 3 and B= Red, Blue
So we have A U B = 1, 2, Red, Blue
Again if A = 1, 3, 5 and B = 2, 3, 4, 6.
So we have A U B = 1, 3, 5, 2, 4, 6.
Also if A= 1, 2 and B = 1, 2.
So we have A U B = 1, 2.
Following are some properties of Union of sets:
a)     A U B = B U A, this property is known as Commutative Property.
b)     A U ( B U C ) = ( A U B ) U C, this property is known as Associative Property.
c)      A U A = A,
d)     A U φ = A,
e)     ‘A’ is the subset of ‘B’ if A U B = B.
Intersection: We can also form a new Set by determining the common elements of the given two sets. This is called Intersection of the two sets.
The intersection of 'A' and 'B', denoted by A «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»§#8745;«/mo»«/math» B
If A  B =φ , then 'A' and 'B' are called disjoint sets.

Topics Covered in Basic Operations On Sets

Union

posted on: 15 Mar, 2012 | updated on: 30 Aug, 2012

Set can be defined as the collection of well defined and distinct objects, considered as an object. While studying Sets theory, we need to reform the group of the sets in order to get the solutions. One of the main applications of the sets theory is to make the Relations between two sets. For making these relations, certain operations can be performed on the Numbers. We will discu...Read More

Complements

posted on: 15 Mar, 2012 | updated on: 04 May, 2012

A Set can be defined as a well organized collection of distinct objects, placed under a group. We sometimes say that a set is the most elementary concept studied in mathematics.
Different mathematical operations can be performed on Sets. When we talk about the complement of a set, it simply means that we want to represent the elements of a universal set, which are not in th...Read More

Cartesian Products

posted on: 15 Mar, 2012 | updated on: 16 Jul, 2012

The Cartesian product of two Sets is defined in terms of ordered pairs. The Cartesian product sets are also called cross join sets in which the product of each row of the first table multiplied by each column of another table. Such situation arises when their exist no relation between the two given tables.
The Cartesian product of sets A and B is defined as the Set o...Read More

Intersection

posted on: 17 Mar, 2012 | updated on: 18 Jun, 2012

We can say that a Set is the collection of different objects grouped together. Any set is the most basic element used in mathematics. In everyday life we observe that Sets are used to make groups of same type of elements. When we study sets theory, we need to re- organize the group of the sets which always helps us to get the solutions. One of the main applications of the s...Read More