# complement of a set | types of set theory | Roster method | universal set

**complement of a set**we give the information about methods of writing sets and

**types of set theory**like Roster method and Set builder methods. also give information about

**Equal sets**, Subset, Disjoint set,

**Universal set.**

## complement of a set:

**Set Definition :**

**“A well defined collection of items is called set.”**

**Examples :**

### Methods of writing sets :

There are two methods of writing sets

**1) Listing method / Roster from**

**2) Rule method / Set builder from**

**I) Listing method / Roster form :**

**For example :**

**Examples :**

**II) Rule method / Set builder form :**

**For example :**

**Examples :**

#### Type of Sets Theory :

**There are 4 types of sets**

**1. Empty set or Null set :**

**2. Singleton Set :**

**3. Finite Set :**

**4. Infinite Set :**

**Important things :**

**Equal sets:**

D = { y | y is a letter of the word ‘silent’.} Therefor, D = { s, i, l, e, n, t}

**Venn diagram**as shown below:

#### Subset:

D is a subset of C which is symbolically written as D ⊆ C. It is read as ‘D is a subset of C’ or ‘D subset C’.

**Ex 1.**

D = {12, 14, 16, 18}

Every element of set D is also an element of set C.

Therefor, D ⊆ C.

**Venn diagram**as shown below:

**Universal set:**

- The Universal set means all elements are inside in the set that is a whole set which will accommodate all the given sets under consideration which in general is known as Universal set.
- So that the sets under consideration are the all subsets of this Universal set.
- Universal set are indicated by using the U latter and use a rectangle box.

**Example:** Suppose we want to study the students in class FY BCA who frequently remained absent. Then we have to think of all the students of class FY BCA who are in the College. So all the students in a school or the students of all the divisions of class FY BCA in the College is the Universal set.

**Disjoint sets:**

Let, P = { 11, 13, 15, 19}

and Q = {22, 24, 28} are given.

Confirm that not a single element is common in set P and Q. These sets are completely different from each other. So the set P and Q are disjoint set.

This can be represented by Venn diagram as shown below: –

**Complement of a set:**

Suppose U is an universal set. If P⊆U, then the set of all elements in U, which are not in set P is called the complement of P. It is denoted by P′.

P′ is defined as follows.

P′ = {x | x ⊂ U, and x ⊄ B}

Ex (1) U = { 41, 42, 43, 44, 45, 46, 47, 48, 49, 50}

P = {42, 44, 46, 48, 50}

P′ = {41, 43, 45, 47, 49}

This can be represented by Venn diagram as shown below: –

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