Sets

A set is a well-defined collection of objects. Another word, it is a collection.
Indicated with curly braces { }
Set can contain numbers, words, even pictures,etc

For example,

1) A = { lion, Tiger, Cheetah, Leopard, Cougar, Ocelot } This is a set of large species of cats.
2) B = { a, b, c...,z } This is a set consisting of the small letters of the English alphabet.
3) C = { -1, -2, -3,... } This is a set of negative numbers.
4) X = { 1, 2, 3,... } This is a set of the positive numbers.
5) Y = { January, February, March,...} This is a set of months of the year.
6) Z = { 🙄, 😝, 😀, 😂}.This is set of emoji. It is best example for set is also containing pictures.

Sets are usually denoted by the Capital letters. A, B, C, X, Y and Z. etc. example- A = { 1, 2, 3,... } , B = { a, b, c,...z} , C = { -1, -2, -3,... } The elements of a set are represented by small letters. ex- { a, b, c,...z }

If "a" is an element of a set A, then we say that "a" belongs to A. The word belongs to denoted by the Greek symbol ∈(epsilon) Thus, in notation form, a belongs to Set A is Written as ' a ϵ A ' and 'b' does not belong to Set 'A' is Written as b ∉ A.
1) if A = { 1, 2, 3, 4, 5}, then 3 ∈ A and 6 ∉ A. because element 6 doesn't present in Set A.
2) if P being the Set of perfect square numbers then 36 ∈ P but 5 ∉ P.

NOTE: Objects, elements and members of a Set are Synonymous terms.

*Representations Of Sets*

Sets are generally represented by following two ways :-

1. Roster Form or Tabular Form or Listing Method
2. Set-Builder Form or Rule Method

Roster form or Tabular Form or Listing Method

In this form, all the elements of a set are listed, the elements are being separated by commas and are enclosed within curly braces { }.
For example,
1) The set of all natural numbers less than 10 is represented in roster form as { 1, 2, 3, 4, 5, 6, 7, 8, 9 }.
2) The set of prime numbers is { 2, 3, 5, 7, ... }. Here, three dots tell us that the list of prime numbers continue indefinitely.

NOTE
1) In roster form, order in which the elements are listed is not important I.e. the set of natural numbers less than 10 can be also written as {2, 4, 1, 3, 5, 6, 8, 7, 9} insted of {1, 2, 3, 4, 5, 6, 7, 8, 9}
2) In roster form, element is not repeated, I.e. all the elements are taken as distinct. e.g. The set of letters forming the word 'MISCELLANEOUS' is {M, I, S, C, E, L, A, N, O, U}