# Are the following relations reflexive/irreflexive/neither? Symmetric/asymmetric/neither? Transitive/intransitive/neither?

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## Which of the following relations is symmetric but neither reflexive nor transitive?

Relation R is not reflexive as (5, 5), (6, 6), (7, 7) ∉ R. Now, as (5, 6) ∈ R and also (6, 5) ∈ R, R is symmetric. ∴R is not transitive. Hence, relation R is symmetric but not reflexive or transitive.

## Which of the following relations is symmetric but neither reflexive nor transitive on a set A ={ 1 2 3?

Hence, relation R is symmetric and transitive but not reflexive.

## Can a relation be reflexive and Irreflexive?

Notice that the definitions of reflexive and irreflexive relations are not complementary. That is, a relation on a set may be both reflexive and irreflexive or it may be neither. The same is true for the symmetric and antisymmetric properties, as well as the symmetric and asymmetric properties.

## Which of the following relation is Irreflexive?

2. Irreflexive Relation: A relation R on set A is said to be irreflexive if (a, a) ∉ R for every a ∈ A.

## Is every symmetric relation reflexive?

No, you’re only considering the diagonal of the set, which is always an equivalence relation. But what if you took R={(1,1),(2,2),(2,1)}? It’s still a valid relation, it’s reflexive on {1,2} but it’s not symmetric since (1,2)∉R. The point is you can have more than just pairs of form (x,x) in your relation.

## Which one is not symmetric relation?

Number of Asymmetric Relations on a set with n elements : 3n(n1)/2. In Asymmetric Relations, element a can not be in relation with itself. (i.e. there is no aRa ∀ a∈A relation.) And Then it is same as Anti-Symmetric Relations.

## Is reflexive relation transitive?

Yes. Such a relation is indeed a transitive relation, since the only relevant cases for the premise “xRy∧yRz” are x=y=z in such relations.

## Can a relation be reflexive and asymmetric?

We get around this by specifying S=∅ and the relation as the empty relation. It is vacuously reflexive and asymmetric.

## Can a relation be symmetric and asymmetric?

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.

## Is every relation transitive?

No, it is not true. The relation R on A is symmetric and transitive.

## Is this relation transitive?

In mathematics, a relation R on a set X is transitive if, for all elements a, b, c in X, whenever R relates a to b and b to c, then R also relates a to c.

## Is reflexive relation symmetric and transitive?

R is reflexive if for all x A, xRx. R is symmetric if for all x,y A, if xRy, then yRx. R is transitive if for all x,y, z A, if xRy and yRz, then xRz. R is an equivalence relation if A is nonempty and R is reflexive, symmetric and transitive.

## Can symmetric relations be transitive?

It is transitive because it lacks any opportunity not to be transitive: you would need to find a,b,c such that a∼b and b∼c but a≁c in order to have a relation that is not transitive. The only way you can say a∼b and b∼c with this relation is if a=b=c. And in that case a∼c holds.

## What is asymmetric relation with example?

In discrete Maths, an asymmetric relation is just opposite to symmetric relation. In a set A, if one element less than the other, satisfies one relation, then the other element is not less than the first one. Hence, less than (<), greater than (>) and minus (-) are examples of asymmetric.

## What is symmetric in relations?

A symmetric relation is a type of binary relation. An example is the relation “is equal to”, because if a = b is true then b = a is also true.

## What is reflexive symmetric antisymmetric transitive?

A relation R that is reflexive, antisymmetric, and transitive on a set S is called a partial ordering on S. A set S together with a partial ordering R is called a partially ordered set or poset. As a small example, let S = {1, 2, 3, 4, 5, 6, 7, 8}, and let R be the binary relation “divides.” So (2,4) R, (2, 6) R, etc.

## What do you mean by asymmetrical?

Definition of asymmetrical
1 : having two sides or halves that are not the same : not symmetrical an asymmetrical design asymmetrical shapes. 2 usually asymmetric, of a carbon atom : bonded to four different atoms or groups.