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.
How to Calculate Number of Antisymmetric Relations on Set A?
Number of Antisymmetric Relations on Set A calculator uses No. of Antisymmetric Relations on A = 2^(Number of Elements in Set A)*3^((Number of Elements in Set A*(Number of Elements in Set A-1))/2) to calculate the No. of Antisymmetric Relations on A, The Number of Antisymmetric Relations on Set A formula is defined as the number of binary relations R on a set A in which there is no pair of distinct or dissimilar elements of A, each of which is related by R to the other, which means for all x and y in A, if (x,y) ∈ R with x ≠ y, then (y,x) ∉ R, or, equivalently, if (x,y) ∈ R and (y, x) ∈ R, then x = y. No. of Antisymmetric Relations on A is denoted by NAntisymmetric Relations symbol.
How to calculate Number of Antisymmetric Relations on Set A using this online calculator? To use this online calculator for Number of Antisymmetric Relations on Set A, enter Number of Elements in Set A (n(A)) and hit the calculate button. Here is how the Number of Antisymmetric Relations on Set A calculation can be explained with given input values -> 12 = 2^(3)*3^((3*(3-1))/2).