## Difference of Sets

The difference of set B from set A, denoted by A-B, is the set of all the elements of set A that are not in set B. In mathematical term, A-B = { x: x∈A and x∉B}

The difference of set B from set A, denoted by A-B, is the set of all the elements of set A that are not in set B. In mathematical term, A-B = { x: x∈A and x∉B}

A set is a collection of distinct objects(elements) which have common property. For example, red, blue, and green are colors. When the elements are considered collectively, set is formed. The elements in a set can be represented in a number of ways, some of which are more useful for mathematical treatment and others for general understanding. These different methods of describing a set are called set notations.

There are many technical terminologies that we need to understand to improve our learning of set theory. Some of them are explained below:

For two sets A and B, the Cartesian product of A and B is denoted by A×B and defined as: A×B = { (a,b) | aϵA and bϵB } Cartesian Product is the multiplication of two sets to form the set of all ordered pairs. The first element of the ordered pair belong to first set and second pair belong the second set. For an example,

Complement of a set A, denoted by Ac, is the set of all elements that belongs to universal set but does not belong to set A. In mathematical form, complement of a set can be expressed as:

A set is a collection of distinct objects(elements) which have common property. For example, cat, elephant, tiger, and rabbit are animals. When, these animals are considered collectively, it’s called set. Set Notation The members(elements) of set is separated by comma and braces { } are used outside the comma separated elements.

For two sets A and B, the union of A and B (denoted by A∪B) is the set of all distinct elements that belong to set A or set B. In mathematical form, A∪B = { x: x∈A or x∈B}

Venn Diagram was proposed in 1880 by John Venn. These diagrams are very useful tools to understand, to interpret and to analyze the information contained by the sets. The different region in the Venn Diagrams can be represented with unique mathematical notation. eg: (AUB), (AUBUC) etc.

The intersection of two sets A and B ( denoted by A∩B ) is the set of all elements that is common to both A and B. In mathematical form, For two sets A and B, A∩B = { x: x∈A and x∈B } Similarly for three sets A, B and C,