Set Theory

A set is defined as a collection of numbers which are arranged in a group. The set with any numbers can be denoted in the symbol braces { }.

For example: The set of numbers are represented as {2, 3, and 4}.

• In basic concepts of set theory, the Set theory contains some of the operations.
• Operations are union, intersection, complement, symmetric difference, Cartesian product and power set.

Union:

• In basic concepts of set theory, the union of the sets A and B, It is denoted by A U B.
• The union operations define set of the all objects in A and B.

Example of Union:

A= {2, 3, 4} B= {2, 3, 4, 5}

A U B = {2, 3, 4, 5}

Intersection:

• In basic concepts of set theory, the intersection of the sets A and B, It is denote by the A ?B.
• This operations are defines set of all objects of the both A and B.

Example of Intersection:

A= {2, 3, 4} B= {2, 3, 4, 5}

A ?B = {2, 3, 4}

Complement:

• In math, the complete operation is the different operation.
• It describes complement of set A relative to set U.

• This operation is denoted by Ac. It means, the set all object of U is not a members of A.

• This operation is also known as set difference.

Example of complement:

U= {1, 2, 3, 4, 5, 6)

A= {1, 2, 3 4, 5}

The complement is Answer is=6.

Totally Bounded set: Here we see about bounded set. It is a set which consists of both upper and lower bound values. If a set is said to be totally bounded, then the set is only bounded.A subset is used to cover the totally bounded set. A totally bounded set contains both the upper and lower bound.

Lower Bound: The lower bound is a set of numbers in bounded set they are lesser than other numbers which are present in the given set.

For example:

If the Interval is (7, 8)

Lower bound = 4

Here, the value 4 is given as the lower bound of given totally bounded set.

Then, we take numbers from 4 to 7 as the lower bound numbers.

4, 5, 6, 7 are the lower bound numbers.

Upper Bound: Upper bound is a set of numbers which are greater than the other numbers of a bounded set.

For example:

When the interval is (5, 9) and the upper bound = 11 for a totally bounded set.

The upper bound value is 11. Then the numbers from 9 to 11 are the upper bound numbers.

Therefore the upper bound numbers are 9, 10, 11 for a totally bounded set.

Thus these are about totally bounded set.

• The Cartesian product is also one of the basic geometry concepts operations.

• In set theory, a new set can be build by associating any element of the single element with the every component of the other set.

• The Cartesian product of two sets A and B and it is indicate by A x B.

• The A x B is the set of the all ordered pairs.

Example of Cartesian product:

{3,4}x{blue, red}={(3,blue), (3,red), (4,blue),(4, red)}.