What is a Relation?
A Relation in mathematics are used to describe a connection between the elements of two sets. They help to map the elements of one set (known as the domain) to elements of another set (called the range) such that the resulting ordered pairs are of the form (input, output). It is is a subset of the cartesian product of two sets. Suppose there are two sets given by X and Y. Let x ∈ X (x is an element of set X) and y ∈ Y. Then the cartesian product of X and Y, represented as X × Y, is given by the collection of all possible ordered pairs (x, y). In other words, a relation says that every input will produce one or more outputs.
What are Symmetric and Antisymmetric Relations?
A relation is said to be a Symmetric Relation if one set, A, contains ordered pairs, (x, y) as well as the reverse of these pairs, (y, x). In other words, if (x, y) ∈ R then (y, x) ∈ R for the relation to be symmetric.
A relation is said to be Antisymmetric Relation for a binary relation R on a set A, if there is no pair of distinct or dissimilar elements of A, each of which is related by R to the other. In a formal way, relation R is antisymmetric, specifically if for all a and b in A, if R(x, y) with x ≠ y, then R(y, x) must not hold, or, equivalently, if R(x, y) and R(y, x), then x = y.
How to Calculate Number of Relations on Set A which are both Symmetric and Antisymmetric?
Number of Relations on Set A which are both Symmetric and Antisymmetric calculator uses No. of Symmetric and Antisymmetric Relations on A = 2^(Number of Elements in Set A) to calculate the No. of Symmetric and Antisymmetric Relations on A, The Number of Relations on Set A which are both Symmetric and Antisymmetric formula is defined as the number of binary relations R on a set A which are both symmetric and antisymmetric. No. of Symmetric and Antisymmetric Relations on A is denoted by NSymmetric & Antisymmetric symbol.
How to calculate Number of Relations on Set A which are both Symmetric and Antisymmetric using this online calculator? To use this online calculator for Number of Relations on Set A which are both Symmetric and Antisymmetric, enter Number of Elements in Set A (n(A)) and hit the calculate button. Here is how the Number of Relations on Set A which are both Symmetric and Antisymmetric calculation can be explained with given input values -> 8 = 2^(3).