Explain Subset ,Power subset , Proper set, Power set ,Universal set ,And many more ... PLEASE Best explanation will b marked as BRAINLIEST.
Give examples also
Answers
Subset
Subsets are a part of one of the mathematical concepts called Sets. A set is a collection of objects or elements, grouped in the curly braces, such as {a,b,c,d}. If a set A is a collection of even number and set B consists of {2,4,6}, then B is said to be a subset of A, denoted by B⊆A and A is the superset of B.
Power Subset
In mathematics, the power set of a set S is the set of all subsets of S, including the empty set and S itself. In axiomatic set theory, the existence of the power set of any set is postulated by the axiom of power set. The powerset of S is variously denoted as P(S), (S), P(S), ℙ(S), ℘, or 2S.
Proper set
A proper subset of a set A is a subset of A that is not equal to A. In other words, if B is a proper subset of A, then all elements of B are in A but A contains at least one element that is not in B. For example, if A={1,3,5} then B={1,5} is a proper subset of A.
Power Set
The power set is a set which includes all the subsets including the empty set and the original set itself. It is also a type of sets. If set A = {x,y,z} is a set, then all its subsets {x}, {y}, {z}, {x,y}, {y,z}, {x,z}, {x,y,z} and {} are the elements of powerset, such as:
Power set of A, P(A) = {x}, {y}, {z}, {x,y}, {y,z}, {x,z}, {x,y,z} and {}
Where P(A) denotes the powerset.
Universal Set
A universal set (usually denoted by U) is a set which has elements of all the related sets, without any repetition of elements. Say if A and B are two sets, such as A = {1,2,3} and B = {1,a,b,c}, then the universal set associated with these two sets is given by U = {1,2,3,a,b,c}.
In Mathematics, the collection of elements or group of objects is called a Set. There are various types of sets like Empty set, Finite set, Infinite set, Equivalent set, Subset, Superset and Universal set. All these sets have their own importance in Mathematics. There is a lot of usage of sets in our day-to-day life, but normally they are used to represent bulk data or collection of data in a database. For example, our hand is a set of fingers, where each finger is different from the other one. The notation of set is usually given by curly brackets, {} and each element in the set is separated by commas like {4, 7, 9}, where 4, 7, and 9 are the elements of sets.