How many symmetric relations are there on a set with n elements

Connect and share knowledge within a single location that is structured and easy to search. The elements of the main diagonal can be perfectly chosen for the relation because they are symmetric. Every relation on a set of N elements can be thought as an NxN matrix.

For a symmetric relation the Matrix is also symmetric. This problem is very similar to Number of relations that are both symmetric and reflexive. Sign up to join this community. The best answers are voted up and rise to the top. Stack Overflow for Teams — Collaborate and share knowledge with a private group. Create a free Team What is Teams? Learn more. Ask Question. Asked 10 years, 11 months ago. Active 1 month ago.

Viewed 48k times. Thank you. Anonymous Anonymous 3 3 gold badges 5 5 silver badges 6 6 bronze badges. Since I don't just want to give the answer, here's a good hint: how many total relations are there for an n-element set, and what do they correspond to?

Determine the elements which should be in R to make R a symmetric relation. The null or empty set is a symmetric relation for every set. Since there are no elements in an empty set , the conditions for symmetric relation hold true. It is possible for a set to be symmetric and antisymmetric but not always.

Learn Practice Download. Symmetric Relations In discrete mathematics, a symmetric relation between two or more elements of a set is such that if the first element is related to the second element, then the second element is also related to the first element as defined by the relation.

What are Symmetric Relations? Asymmetric, Anti-symmetric and Symmetric Relations 3. Number of Symmetric Relations 4. Asymmetric, Anti-symmetric and Symmetric Relations. Hence, R is not a symmetric relation. Solution: To make R a symmetric relation, we will check for each element in R. Count number of triplets with product equal to given number with duplicates allowed Set Permutation of a number whose sum with the original number is equal to another given number.

Minimum number of moves to make M and N equal by repeatedly adding any divisor of number to itself except 1 and the number. Print all numbers whose set of prime factors is a subset of the set of the prime factors of X. Article Contributed By :. Easy Normal Medium Hard Expert. Writing code in comment? Please use ide. Load Comments. What's New. Most popular in Combinatorial.