Types of Sets:

1. Empty Set (Null Set)

• Definition: A set with no elements.

• Notation: ∅ or { }

• Example: The set of square circles: ∅

2. Finite Set

• Definition: A set with a countable number of elements.

• Example: A={1,2,3,4,5}

3. Infinite Set

• Definition: A set with an uncountable or limitless number of elements.

• Example: The set of natural numbers: N={1,2,3,… }

4. Equal Sets

• Definition: Two sets with exactly the same elements.

• Example: A={1,2,3} B={3,1,2} , Here A = B

5. Equivalent Sets

• Definition: Sets with the same number of elements (cardinality), not necessarily the same elements.

• Example: A={a, b, c}, B={1,2,3}

6. Subset

• Definition: Set A is a subset of B if every element of A is also in B.

• Notation: A⊆B

• Example: (i) A={1,2}, B={1,2,3} (ii) A={1,2, 3}, B={1,2,3}

7. Proper Subset

• Definition: A subset that is not equal to the original set.

• Notation: A ⊂ B

• Example: A={1,2}, B={1, 2, 3}

8. Universal Set

• Definition: A set that contains all the elements under consideration.

• Notation: U

• Example: Set of Natural Numbers

9. Power Set

• Definition: The set of all subsets of a given set.

• Notation: P(A)

• Example: A={1,2} then P(A)={∅,{1},{2},{1,2}}

10. Disjoint Sets

• Definition: Sets that have no elements in common.

• Example: A={1,2}, B={3,4}

11. Overlapping Sets

• Definition: Sets that share at least one common element.

• Example: A={1,2,3},B={3,4,5}

12. Singleton Set

• Definition: A set with exactly one element.

• Example: A={7}