What is the difference between reflexive symmetric and transitive relations?

What is the difference between reflexive symmetric and transitive relations?

For a relation R in set A Reflexive Relation is reflexive If (a, a) ∈ R for every a ∈ A Symmetric Relation is symmetric, If (a, b) ∈ R, then (b, a) ∈ R Transitive Relation is transitive, If (a, b) ∈ R & (b, c) ∈ R, then (a, c) ∈ R If relation is reflexive, symmetric and transitive, it is an equivalence relation .

How do you know if a relation is transitive?

Transitive Relation is transitive, If (a, b) ∈ R & (b, c) ∈ R, then (a, c) ∈ R If relation is reflexive, symmetric and transitive, it is an equivalence relation .

What is the difference between transitive relation and equivalence relation?

Relation is transitive, If (a, b) ∈ R & (b, c) ∈ R, then (a, c) ∈ R If relation is reflexive, symmetric and transitive, it is an equivalence relation.

What is a reflexive relation?

A reflexive relationis a binary relation on a set for which every element is related to itself. As you can clearly see $(0,0),(1,1)$ etc. are not contained in your relation, so it is not reflexive.

What is the difference between symmetric property and reflexreflexive property?

Reflexive Property The Reflexive Property states that for every real number x , x = x . Symmetric Property The Symmetric Property states that for all real numbers x     and     y , if x = y , then y = x .

What is an example of a non symmetric relation?

A relation R is non-symmetric iff it is neither symmetric nor asymmetric. For example, loves is a non-symmetric relation: if John loves Mary, then, alas, there is no logical consequence concerning Mary loving John. Reflexivity. A relation R is reflexive iff, everything bears R to itself.

What is the difference between symmetric property and transitive property?

The Symmetric Property states that for all real numbers x and y , if x = y , then y = x . The Transitive Property states that for all real numbers x , y, and z,