Set Theory

What is a Set??

A well-defined collection of distinct objects is called a set.Although any type of object can be collected into a set, set theory is applied most often to objects that are relevant to mathematics.

Below is the Notation of Sets

Capital letters are usually used to denote or represent a set.
viz., A, B, C, D, . . . .

The elements of sets are usually represented by lower case letters.
viz., a, b, c, x, y

There are two methods by which a set is represented.

• Roster Method
• Set builder form.

Roster Method: Here, a set is represented by listing all the elements of the set, the elements being separated by commas and are enclosed within flower brackets { }. It is also called as Tabular Method.

Example: A set containing 3,5,7,9,11 is written as {3,5,7,9,11} in Roster Method.

Set Builder Form: In set builder form, a set is represented by stating all the properties which are satisfied by the elements of the set and not by any other element. It is also called as Property Method.
If A contains all values of 'x' for which the condition P(x) is true, then we write A = {x: P(x)}.
Example: If A is a set of all positive factors of 36, then in Set builder method it is written as

A = {x : x is a factor of 36, x Î N}

Sub Set:
If all the members of set A are also members of set B, then A is a subset of B, denoted A ⊆ B.
For problems on Subsets please click here.