# Set Operations.

The Process of making a new sets from two or more given sets applying some special rules is known as set operations.

If we are given two sets , then there are three standard ways to construct new sets from them. The three operations are called binary set operations , which are as following:

**Union:**

** ** A set that contains all the elements contained by first set (A) and second set (B) is known as union of the two sets (A and B).

We denote union of two sets (A and B) by symbol A ∪ B.

For example: if A={1,2,3} and B={3,4,5} Then,

A ∪ B={1,2,3,4,5}

**Intersection:**

** **A set whose elements are the common elements of two sets (A and B) is known as the intersection of the sets(A and B). The intersection of two sets (A and B) is denoted by the symbol A ∩ B.

For example: If A={1,2,3} and B={2,3,4} Then A∩B={2,3}

**Complement: **

** **A set whose elements are all the elements of universal set except a set (A)is known as the complement of the set (A).** **The complement of a set (A) is denoted by symbol Â and read as “A complement”

For example: If A={1,2,3} , B={3,4,5} and C={4,5,6,7} Then , Â={4,5,6,7}

**Difference:**

** **** **The difference of set A and B is the set formed by a set with all elements of set A that does not belongs to set B. We denote the difference of set A and B by A-B and difference if set B and A by B-A.

For example: If A={1,2,3,4} and B={3,4,5,6} then,

A-B={1,2} , B-A={5,6} , A-A= φ and B-B= φ

Above set operations are shown below as graphical representation in Venn diagram.

**Union:**

In the following figures A∪B is shown as shaded region:

**Intersection:**

In the following figures A∩B is shown as shaded region , in second figure no region is shaded because in the figure A∩B=Φ

**Complement:**

In the folowing figure Â is shown by shaded region:

**Difference:**

In the first figure below A-B is shown as shaded region and in second figure A-A is shown and no region as shaded as A-A is Φ

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