Types of Sets

Any collection of things (elements) in logic and mathematics, which may or may not be scientific (e.g., numbers, functions). The intuitive concept of a set is likely older than the concept of a number. Individuals of a herd of cattle, for example, maybe be paired with rocks in a bag without any of the individuals in either group being numbered.

The concept goes on indefinitely. The set containing integers between 1 to 100, for example, is finite, but the collection of all integers is unlimited. A listing of all of its members contained in braces is a popular representation of a set. A collection without output from any members is known as an unfilled, or null set and is represented by the symbol ∅. 

The number of items in a set determines what type of set it is. Sets are groups of components that are of the same kind. For instance, a collection of positive integers, natural numbers, and so on. Let’s discuss the types of sets in detail:

Types of sets

• Unit sets

A set that contains only one set or a single set is known as a singleton or unit set. Because it just contains one element, it’s also called a unit set. Set A = {k | k is an integer between 3 and 5}, resulting in A = {4}.

• Finite sets

A finite set is one with a finite or precise countable number of items, as the name indicates. It’s termed a non-empty limited set if the set isn’t empty. The following are some instances of finite sets: Set B ={ k | k is an even integer less than 10, for example, is B = {2,4,6,8,10}. Consider the following example: Set A = x: x is just a day in January }; Set A will consist of  31 entries.

• Infinite set

An infinite set is a set containing an unlimited number of items. To put it another way, if a set is just not finite, it will be endless. For example, A = {x: x is a natural number}, and natural numbers are infinite. As a result, A is an infinite set.

Let’s look at another example: Set B = {z: z is the point on the number line}; A number line has an unlimited number of points. As a result, B is an infinite set in this case.

Set C = {Multiples of 6} is another example. We can have an endless number of multiples of 6 here.

• Null set

This is another type of set, A set is known as both null sets as well as an empty set because the usually does not contain any elements in the set. ∅ this is the symbol that we generally use to represent or show an empty set. It’s pronounced ‘phi.’ Set X = {} as an example.

• Equal set

When two pairs contain the same items, they are referred to be equal sets. A = {5,6,7,8,9} and B = {9,8,7,6,5} are two examples. Sets A and B are equivalent in this case. A = B can be used to express this.

• Unequal set

Unequal sets are those that have at most 1 element that is different. A ={7,8,9} and B = {9,10,11} are two examples. In this case, we can say that set A and set B  are unequal sets. X Y can be used to symbolise this.

• Equivalent sets

When two sets contain the same number of items but distinct elements, they are shown to be equivalent sets. A = {1,2,3,4}; B ={a,x,y,z};  Because n(A) = n(B), sets A and B are equal sets.

• Overlapping sets

If at minimum one element of set A appears in set B, the two pairs are shown to overlap. A ={8,9,10} B = {4,7,10} is an example. Element 4 appears in both sets A and B in this case. As a result, Both A and B are two sets that overlap.

• Disjoint sets

If there are no shared items in both sets, they are disjoint sets. A = {11,12,14,16}; B = {7,8,9,10}; both Sets A and B become disjoint in this case.

• Subset

If every member in set A is also present in set B, set 

A is a subset of set B(A ⊆ B), and set B is indeed the superset of set A(B ⊇ A).

Because all of the components in set A are present in set B, A = {1,2,3} B = {1,2,3,4,5,6}.

as we find all elements in set A, it can be denoted as A ⊆ B.

• Universal set

If a set is containing all the items of the specific topic, the particular set is said to be a universal set. The letter ‘U’ is used to signify a universal set in set notation. Let U stand for {The list of the all-road transport vehicles}.” This universal set includes a set of automobiles, a set of cycles, and a set of trains, all of which are a subset of this set.

Conclusion

In this article, we have covered what is a set, detailed information of the set, types of sets, and the examples are also being covered along with the types of sets. set is a topic that can be applied both in the field of mathematics as well as in the field of logic.