Notes on Sets

Definition of Set

• A set is a well-defined collection that contains different objects.
• A set is always denoted by capital letters (like A, B) and written in curly brackets.

Characteristics of Set

• A set must be well-defined.
• Example:
  • If we ask "Who are the top 5 cricketers in India?" the answers may vary.
  • But if we ask "What are the natural numbers less than 10?" the answer will always be from 1 to 9.

Types of Sets

1. Empty Set

   • It contains no elements.

   • It is represented by

     or
     • {}.
   • Example: x is an even number greater than 2.

2. Finite Set

   • It has a countable number of elements.
   • Example: {1, 2, 3, 4, 5, 6} (This is a set of 6 elements).

3. Infinite Set

   • It has uncountable elements.
   • Example: the set of natural numbers.
   • Like {1, 2, 3, ...}.

4. Singleton Set

   • It contains only one element.
   • Example: {1} or {2}.

5. Equal Set

   • When two sets have the same elements, they are said to be equal.
   • Example:
     • A = {1, 2, 3, 4}
     • B = {3, 4, 1, 2}
     • C = {2, 1, 3, 4}
   • All have the same elements, so A = B = C.

Conclusion

• Today we learned about sets and their various types.
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