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 Reflexive and Symmetric Relations?
A Reflexive Relation on a Set is a binary relation that holds for every element of the set. In other words, a Reflexive Relation is one in which every element is related to itself, which means for all x ∈ A, (x,x) ∈ R.
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.
How to Calculate Number of Relations on Set A which are both Reflexive and Symmetric?
Number of Relations on Set A which are both Reflexive and Symmetric calculator uses No. of Reflexive and Symmetric Relations on A = 2^((Number of Elements in Set A*(Number of Elements in Set A-1))/2) to calculate the No. of Reflexive and Symmetric Relations on A, The Number of Relations on Set A which are both Reflexive and Symmetric formula is defined as the number of binary relations R on a set A which are both reflexive and symmetric. No. of Reflexive and Symmetric Relations on A is denoted by NReflexive & Symmetric symbol.
How to calculate Number of Relations on Set A which are both Reflexive and Symmetric using this online calculator? To use this online calculator for Number of Relations on Set A which are both Reflexive and Symmetric, 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 Reflexive and Symmetric calculation can be explained with given input values -> 2 = 2^((3*(3-1))/2).