## What is symmetric relation in discrete mathematics?

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 do you mean by symmetric relation?

Symmetric Relation In a symmetric relation, if a=b is true then b=a is also true. In other words, a relation R is symmetric only if (b, a) ∈ R is true when (a,b) ∈ R. An example of symmetric relation will be R = {(1, 2), (2, 1)} for a set A = {1, 2}. So, for a symmetric relation, aRb ⇒ bRa, ∀ a, b ∈ A.

#### What are relations in discrete mathematics?

In discrete mathematics, the relation can be described as a collection of ordered pairs. It is used to relate an object from one set to the other set, and the sets must be non-empty. The relation can contain two or more than two sets. Suppose there are two sets, A and B for instance.

**How do you find the number of symmetric relations?**

Total number of symmetric relations is 2n(n+1)/2.

**Can relations be symmetric and antisymmetric?**

There is at most one edge between distinct vertices. Some notes on Symmetric and Antisymmetric: • A relation can be both symmetric and antisymmetric. A relation can be neither symmetric nor antisymmetric.

## What is not symmetric relation?

Relation R on a set A is asymmetric if(a,b)∈R but (b,a)∉ R. Relation R of a set A is antisymmetric if (a,b) ∈ R and (b,a) ∈ R, then a=b. “Is equal to” is a symmetric relation, such as 3 = 2+1 and 1+2=3. “Is less than” is an asymmetric, such as 7<15 but 15 is not less than 7.

### What is symmetric relationship in math?

Symmetric Relation. Any relation R in a set A is said to be symmetric if (a, b) ∈ R. This implies that \\[(b, a) ∈ R\\] In other words, a relation R in a set A is said to be in a symmetric relationship only if every value of a,b ∈ A, (a, b) ∈ R then it should be (b, a) ∈ R.

#### What is relations in discrete mathematics?

Discrete Mathematics – Relations. Whenever sets are being discussed, the relationship between the elements of the sets is the next thing that comes up.

**What is antisymmetric relation in Discrete Math?**

Antisymmetric Relation — Discrete Math #5 — Transitive Relation If R is a relation on A, then R is transitive if (a,b) and (b,c) then (a,c) are in R. In other words, for every undirected path joining three vertices a,b, and c, in that order, there is also a directed line joining a to c.

**How to find the number of symmetric relations on a set?**

The number of symmetric relations on a set with the ‘n’ number of elements is given by N = 2n(n+1)/2, where N is the number of symmetric relations and n is the number of elements in the set.