# Set Theory

**SET:**

A

A set can be defined in two ways:

**set**is a collection of clearly defined things, symbols or objects. Each object in a set is called an**element**of the set. A set should always be properly defined.A set can be defined in two ways:

- A set can be defined by listing all its elements for example,

A = {1, 2, 5, 7, 8} - By describing the elements of the set for example,

I = {x : x is an integer, x > 2}

We have to describe a particular property which all the elements x, in a set satisfy
so that one can know whether a particular element belongs to the set.

An element of a set is denoted by symbol
and
denotes "is not an element of" or "does not belong to" for example,

If A= {2, 5, 7} then 2 A and 3 A

If A= {2, 5, 7} then 2 A and 3 A

**NULL SET:**

A set which does not contain any element is called a

**null**set or empty set. It is denoted by the symbol Φ or { }.
Some examples of null set are: The set of triangles with 4 sides, the set of cars
with 2 wheels, the set of cats with 6 legs etc.

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