Concept of Sets

The number of elements in a set determines what type of set it is. Sets are groups of components that are of the same type. For instance, a collection of prime numbers, natural numbers, and so on. Unit sets, finite and infinite sets, empty sets, equal and unequal sets, and so on are all examples of sets. Let’s take a closer look at the various types of sets.

Types of sets 

A set is a well–defined collection of items, as we all know. Depending on the nature of the objects and their properties. There are several different sorts of sets. Some of these are discussed further down. Let’s look at the many sorts of sets and see some examples.

Unit Sets / Singleton Sets

A singleton set is a set that only has one element. It is also called a unit set, when the set contains one element. Set A = k | k is an integer between 5 and 7, resulting in A = 6.

Sets that are finite

A finite set is one with a finite or exact countable number of elements, as the name indicates. If the set is non empty, it is called a non empty finite set . The following are some examples of finite sets: Set B = k | k is an even integer less than 20, for example, is B = 2,4,6,8,10,12,14,16,18. Consider the following example: Set A = x: x is a weekday; Set A will have 7 entries.

Uneven Sets

Unequal sets are those that have at least one element that is different.

X = 4, 5, 6 and Y = 2,3,4 are two examples.  In this case, Sets X and Y are unequal sets . X Y can be used to symbolize this.

Infinite Sets are a type of set that has no end.

An infinite set is a set containing an unlimited number of items. To put it another way, if a set is not finite, it will be endless. For example, A = x: x is a real number, and real numbers are infinite. As a result, A is an infinite set. Let’s look at another example: Set B = z: z is the coordinate of a point on a straight line; a straight line has an infinite number of points. As a result, B is an infinite set in this case. Set C = ‘Multiples of 3’ is another example. We can have an endless number of multiples of 3 here.

Sets that are empty or null

When a set contains no elements, it is called an empty set or null set. The symbol ” is used to represent an empty set. It’s pronounced ‘phi.’ Set X = as an example.

Sets of Equivalents

When two sets contain the same number of elements but distinct elements, they are said to be equivalent sets. A = 7, 8, 9, 10; B = a,b,c,d; C = a,b,c,d; D = a,b,c,d Because n(A) = n(B), sets A and B are equivalent (B)

Sets that cross each other

If at least one element from set A appears in set B, the two sets are said to overlap. A = 4,5,6 B = 4,9,10 is an example. Element 4 appears in both sets A and B in this case. As a result, A and B are two sets that overlap.

Sets of equals

When two sets contain the same items, they are referred to as equal sets. A = 1,3,2 and B = 1,2,3 are two examples. Sets A and B are equal in this case. A = B can be used to represent this.

Subsets and supersets are two types of sets.

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 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 A B.

Set B is the superset of set A, as denoted by B A.

Sets that aren’t connected

If there are no shared elements in both sets, they are disjoint sets. A = 1,2,3,4; B = 7,8,9,10;  B Sets A and B are disjoint in this case.

 Universal Set

A universal set is a collection of all items related to a specific topic. The letter ‘U’ is used to signify a universal set in set notation. Let U stand for “the list of 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 subsets of this universal set.

Sets of Power

The collection of all subsets that a set might contain is called a power set. Example: Set A equals 1,2,3. = {{∅}, {1}, {2}, {3}, {1,2}, {2,3}, {1,3}, {1,2,3}}.

Conclusion 

A set is nothing more or less than a collection of items. Set theory is one of the fundamental building blocks for advanced mathematics, hence it’s important to grasp the fundamentals. Types of sets : Finite Set, Infinite Set, Subset, Proper Subset, Universal Set, Empty Set or Null Set, Singleton Set or Unit Set, Equal Set.