Introduction to Sets and Their Types

Sep 8, 2024

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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