In our day-to-day lives, we classify objects into groups based on their properties. For example, we make a group of daily wear or casual wear and much more. These groups are made by a “collection” of things. Similarly, in mathematics, a set is a “collection”. These sets are denoted by using letters from the English language.
In algebra, a set is a collection of objects and is denoted by using capital letters from the English language. Sets are represented with brackets – { }. These sets can be of various things like shapes, people, numbers, variables, and much more. visit here
For example, a collection of numbers less than 5 can be denoted as, Set N = {0, 1, 2, 3, 4, 5}.
Types of Sets
There are various classifications of sets, these include:
- Finite Sets: Finite Sets are those sets that have a fixed number of elements. For example, odd numbers less than 10 can be denoted as, Set O = {1, 3, 5, 7, 9}.
- Infinite Sets: Infinite Sets are those sets that don’t have a fixed number of elements. For example, Set M = {Whole Numbers}.
- Empty or Null Sets: Empty Sets are sets that do not contain any element. It is expressed with the help of ‘phi’ (∅). For example, Set A = { }.
- Equal Sets: Two sets are considered as equal sets when the elements in the sets are equal. For example, Set W = {4, 5, 6} and Set N = {4, 5, 6}.
- Unequal Sets: Two sets are considered unequal sets when one or more elements are different from each other. For example, Set W = {4, 5, 6} and Set N = {6, 7, 8}.
- Equivalent Sets: Two sets are considered equivalent sets when the number of elements in them is identical. For example, Set A = {1, 2, 3, 4} and Set B = {m, n, o, p}. Since both sets have four elements each, they are considered to be equivalent sets.
- Overlapping Sets: Two sets are considered to be overlapping sets when at least one element from one set is present in the other set and vice versa. For example, Set M = {1, 2, 3, 4} and Set N = {3, 5, 6}. Since element 3 is present in both sets, these sets are considered to be overlapping sets.
- Disjoint Sets: Disjoint Sets are the opposite of Overlapping Sets. In simpler words, disjoint sets have no common elements. For example, Set M = {1, 2, 3, 4} and Set N = {5, 6, 7, 8}. Since there are no common elements in these two sets, these sets are called disjoint sets.
- Subset and Superset: Let us consider two sets M and N. If all the elements of M are there in N, then M is considered to be a subset, and N is considered to be a superset. For example, Set M = {4, 5, 6} and Set N = {4, 5, 6, 7, 8}. Here M is the subset and N is the superset.
- Universal Sets: Universal Set refers to a set that contains all objects of a particular theory, subject or context. For example Set U = {list of all flowers in India}.
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