Types of Sets in Discreate Mathematics
1. Null Set: A set containing no elements is called a null set or an empty set, denoted by ∅.
Example: A = {x / x is a person having age 200} = ∅
2. Singleton Set: A set consisting of only one element is called a singleton set or a unit set.
Example: A = {123}
3. Universal Set: A set containing all elements of all subsets is called a universal set, denoted by U.
Example: If A = {1, 2, 3} and B = {4, 5, 6}, then U = {1, 2, 3, 4, 5, 6}
4. Disjoint Set: Sets A and B are called disjoint if they have no common elements.
Example: In the above example, sets A and B are disjoint.
5. Superset: If A ⊆ B, then B is the superset of A, and A is a subset of B.
Example: If A = {1, 2, 3} and U = {1, 2, 3, 4, 5, 6}, then U is the superset because A ⊆ U.
6. Equal Set: Sets A and B are equal sets if A ⊆ B and B ⊆ A.
7. Equivalence Set: Sets A and B are called equivalence sets if they have the same number of elements.
Example: If A = {1, 2, 3} and B = {4, 5, 6}, then |A| = 3 and |B| = 3, hence A and B are equivalence sets.
8. Power Set (P(A)): A set A is called the power set of A, denoted by P(A), if it contains all subsets of A, including A itself.
Example: If A = {0, 1, 2}, then P(A) = {{0}, {1}, {2}, {0, 1}, {0, 2}, {1, 2}, {2, 0}, {0, 1, 2}}
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