Question

Write an example of transitive relation.

Answer 1

A relation R on set A is called a transitive relation if $(a,b)\in R,(b,c)\in R=>(a,c)\in Rforalla,b,c\in A.$

For example, ‘is congruent to’ is a transitive relation defined on the set of triangles. If triangle ABC is congruent to triangle PQR and triangle PQR is congruent to triangle XYZ, then triangle ABC is congruent to triangle XYZ.

‘is equal to $(=)$‘ is a transitive relation defined on a set of numbers. If $x=yandy=z,thenx=z.$