math

1. SETS
They are a collection of well-defined objects or elements. A set is
represented by a capital letter symbol and the number of
elements in the finite set is represented as the cardinal number
of a set in a curly bracket {…}. For example, set A is a collection of
all the natural numbers, such as A = {1,2,3,4,5,6,7,8,…..∞}

2. FORMULAS OF SETS

3. Roster Form
Listing the elements of a set inside a pair of braces { } is
called the roster form.
(i) Let A be the set of even natural numbers less than 11.
In roster form we write A = {2, 4, 6, 8, 10}
(ii) A = {x : x is an integer and- 1≤ x < 5}
In roster form we write A = {-1, 0,1, 2, 3, 4}

4. Set Builder Form
Set-builder notation is a notation for describing a set by indicating
the properties that its members must satisfy.
Reading Notation :
‘|’or ‘:’ such that
A = { x : x is a letter in the word dictionary }
We read it as
“A is the set of all x such that x is a letter in the word dictionary”
For example,
(i) N = "x : x is a natural number,
(ii) P = "x : x is a prime number less than 100,
(iii) A = "x : x is a letter in the English alphabet,

5. What are the types of Sets?
A set has many types, such as;
1.Empty Set or Null set: It has no element present in it.
Example: A = {} is a null set.
2.Finite Set: It has a limited number of elements. Example: A =
{1,2,3,4}
3.Infinite Set: It has an infinite number of elements. Example: A
= {x: x is the set of all whole numbers}
4.Equal Set: Two sets which have the same members. Example:
A = {1,2,5} and B={2,5,1}: Set A = Set B
5.Subsets: A set ‘A’ is said to be a subset of B if each element of
A is also an element of B . Example: A={1,2}, B={1,2,3,4}, then A
⊆ B

6. P - denoting the set of all primes.
N - denoting the set of all natural
numbers.
Z - denoting the set of all integers.
z⁺- denoting the set of all positive
integers.
Q - denoting the set of all rational
numbers.
Q⁺- denoting the set of all positive
rational numbers.

7. THANKYOU