0
What is the total number of reflexive and symmetric relations on a set containing n elements?
Wiki User
∙ 12y ago
the total no of reflexive relation on an n- element set is 2^(n^2-n).
Wiki User
∙ 12y ago
Add your answer:
Earn +20 pts
How do you Derive The Number of reflexive relation of a Set 's' having n elements?
make a table as I did below for the set {a,b,c} with 3 elements. A table with all n elements will represent all the possible relations on that set of n elements. We can use the table to find all types of relations, transitive, symmetric etc. | a | b | c | --+---+---+---+ a | * | | | b | | * | | c | | | * | The total number of relations is 2^(n^2) because for each a or b we can include or not include it so there are 2 possibilities and there are n^2 elements so 2^(n^2) total relations. A relation is reflexive if contains all pairs of the form {x,x) for any x in the set. So this is the diagonal of your box. THESE ARE FIXED! No, in reflexive relation we still can decide to include or not include any of the other elements. So we have n diagonal elements that are fixed and we subtract that from n^2 so we have 2^(n^2-n) If you do the same thing for symmetric relations you will get 2^(n(n+1)/2). We get this by picking all the squares on the diagonal and all the ones above it too.
How do you Derive The Number of symetric relation of a Set 's' having n elements?
2^(n^2+n)/2 is the number of symmetric relations on a set of n elements.
What is meant by symmetric reflexive and transitive property and also equivalence relation?
First, let's define an equivalence relation. An equivalence relation R is a collection of elements with a binary relation that satisfies this property:Reflexivity: ∀a ∈ R, a ~ aSymmetry: ∀a, b ∈ R, if a ~ b, then b ~ aTransitivity: ∀a, b, c ∈ R, if a ~ b and b ~ c, then a ~ c.
What are equivalence relations?
An equivalence relation r on a set U is a relation that is symmetric (A r Bimplies B r A), reflexive (Ar A) and transitive (A rB and B r C implies Ar C). If these three properties are true for all elements A, B, and C in U, then r is a equivalence relation on U.For example, let U be the set of people that live in exactly 1 house. Let r be the relation on Usuch that A r B means that persons A and B live in the same house. Then ris symmetric since if A lives in the same house as B, then B lives in the same house as A. It is reflexive since A lives in the same house as him or herself. It is transitive, since if A lives in the same house as B, and B lives in the same house as C, then Alives in the same house as C. So among people who live in exactly one house, living together is an equivalence relation.The most well known equivalence relation is the familiar "equals" relationship.
Community problem at list 5 problem?
Five problems that communities must concern themselves with are: affordable housing, crime, power outages, relations between diverse elements, and the education facilities in the community.
What is the possible no of reflexive relations on a set of 5 elements?
The total no. of reflexive relations on a set A having n elements is 2^n(n-1).Thus, the required no. is 2^20 = 1 048 576
How many symmetric relations are there on a set with eight elements?
2^32 because 2^(n*(n+1)/2) is the no of symmetric relation for n elements in a given set
What is the possible number of symmetric relations on a set of 5 elements?
The number is 5! = 120
How do you Derive The Number of reflexive relation of a Set 's' having n elements?
make a table as I did below for the set {a,b,c} with 3 elements. A table with all n elements will represent all the possible relations on that set of n elements. We can use the table to find all types of relations, transitive, symmetric etc. | a | b | c | --+---+---+---+ a | * | | | b | | * | | c | | | * | The total number of relations is 2^(n^2) because for each a or b we can include or not include it so there are 2 possibilities and there are n^2 elements so 2^(n^2) total relations. A relation is reflexive if contains all pairs of the form {x,x) for any x in the set. So this is the diagonal of your box. THESE ARE FIXED! No, in reflexive relation we still can decide to include or not include any of the other elements. So we have n diagonal elements that are fixed and we subtract that from n^2 so we have 2^(n^2-n) If you do the same thing for symmetric relations you will get 2^(n(n+1)/2). We get this by picking all the squares on the diagonal and all the ones above it too.
What is the possible number of reflexive relations on a set of 5 elements?
2 power 20
How do you Derive The Number of symetric relation of a Set 's' having n elements?
2^(n^2+n)/2 is the number of symmetric relations on a set of n elements.
What is the largest equivalence relation on a set A?
An equivalence relation on a set is one that is transitive, reflexive and symmetric. Given a set A with n elements, the largest equivalence relation is AXA since it has n2 elements. Given any element a of the set, the smallest equivalence relation is (a,a) which has n elements.
What is the definition of a symmetric matrix?
Symmetric Matrix:Given a square matrix A such that A'=A, where A' is the transpose of A, then A is a symmetric matrix.note: No need to think about diagonal elements, they can be anything.
What is the definition of a matrix?
Symmetric Matrix:Given a square matrix A such that A'=A, where A' is the transpose of A, then A is a symmetric matrix.note: No need to think about diagonal elements, they can be anything.
what is the definition of The Matrix?
Symmetric Matrix:Given a square matrix A such that A'=A, where A' is the transpose of A, then A is a symmetric matrix.note: No need to think about diagonal elements, they can be anything.
What is the definition of an anti-symmetric matrix?
The Definition of an Anti-Symmetric Matrix:If a square matrix, A, is equal to its negative transpose, -A', then A is an anti-symmetric matrix.Notes:1. All diagonal elements of A must be zero.2. The cross elements of A must have the same magnitude, but opposite sign.
What is meant by symmetric reflexive and transitive property and also equivalence relation?
First, let's define an equivalence relation. An equivalence relation R is a collection of elements with a binary relation that satisfies this property:Reflexivity: ∀a ∈ R, a ~ aSymmetry: ∀a, b ∈ R, if a ~ b, then b ~ aTransitivity: ∀a, b, c ∈ R, if a ~ b and b ~ c, then a ~ c.
