Transitive Irreflexive Relations

In this class, We discuss Transitive Irreflexive Relations.

The reader should have prior knowledge of reflexive property. Click Here.

Transitive Relation:

A relation is said to be transitive if xRy and yRz, then xRz

Example:

A = {1, 2, 5, 7}

R1 = {(1,2), (2,5), (1, 5)}

Relation R1 is a Transitive relation.

R2 = {(1,2), (1,5), (1,1)}

Relation R2 is a transitive relation.

R3 = {(1, 2), (2, 2)}

Relation R3 is a transitive relation.

R4 = {(1, 5), (5, 7)}

Relation R4 is not a transitive relation.

Irreflexive relation:

A relation is said to be irreflexive if, for every x ∈ X, the ordered pair (x, x) should not belong to relation.

Example:

A = {1, 2, 5}

R1 = {(1, 2), (2, 1)}

Relation R1 is a irreflexive relation.

R2 = {(1, 2), (1,5), (1, 1)}

Relation R2 is not irreflexive.