# Mathematics - Sets

Sets class 11 is generally a collection of objects. It is well defined. Set is described by a capital letter.

## Elements of a Set

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

As we represent a set as a capital letter. A is a set that contains five elements, like 1, 2,3,4,5. These elements cannot be repeated. All the elements are represented in a small letter. The set's cardinal number is as follows:

• N: Set of all natural numbers
• Z: Set of all integers
• Q: Set of all rational numbers
• R: Set of all real numbers
• Z+: Set of all positive integers

## Forms of Set

Set is represented in three forms. These are:

Roster form: A = {2, 4, 6, 8, 10, 12}

Statement form: A set of even numbers is less than 16.

Set Builder form: A = {x: x=2n, n ∈ N and 1 ≤ n ≤ 16}

## Properties of Sets

A∪B = B∪A

A∩B = B∩A

### Distributive Property:

A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C)

A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C)

### Associative Property:

A ∪ (B ∪ C) = (A ∪ B) ∪ C

A ∩ (B ∩ C) = (A ∩ B) ∩ C

### De Morgan’s Law:

Law of union: (A ∪ B)’ = A’ ∩ B.’

Law of intersection: (A ∩ B)’ = A’ ∪ B.’