Theory:

Finite set: A set that has a finite number of elements is called finite set.
Example:
  • The set of positive integers less than \(50\).
  • The set of prime factors of \(275\).
  • The set of vowels in alphabets.
  • The set of keys on the laptop.
Infinite set: A set that has an infinite number of elements is called an infinite set.
Example:
  • The set of rational numbers.
  • The set of powers of \(2\).
  • The set of multiples of \(6\).
  • The collection of all even integers.
Set notation: A set is denoted by capital letters English alphabets \(A, B, C, D,...\)
Elements: Elements of the sets are denoted by small letters English alphabets \(a, b, c,...\)
Also, elements of the set should be written inside the curly brackets .
Important!
Suppose the element \(x\) lies in the set \(A\), then we can say that as \(x\) belongs to the set \(A\). That is, \(x\)\(A\).
 
Suppose the element \(x\) doesn't lie in the set \(A\), then we can say that \(x\) does not belong to the set \(A\). That is, \(x\) \(A\).
Example:
Consider the set A=2,4,6,8,10.
 
Here \(2\) is an element of \(A\). That is 2A.
 
\(4\) is an element of \(A\). That is 4A.
 
\(6\) is an element of \(A\). That is 6A.
 
\(8\) is an element of \(A\). That is 8A.
 
\(10\) is an element of \(A\). That is 10A.
 
But the element \(5\) doesn't belong to \(A\). That is 5A.