Definition 3 A relation R in a set A is called
(i)
reflexive, if (a, a) ∈ R, for every a ∈ A,
(ii)
symmetric, if (a1, a2) ∈ R implies that (a2, a1) ∈ R, for all a1, a2 ∈ A (iii)
transitive, if (a1, a2) ∈ R and (a2, a3) ∈ R implies that (a1, a3) ∈ R, for all a1, a2,
a3 ∈ A Rationalised 2023-24
RELATIONS AND FUNCTIONS
3
Definition 4 A relation R in a set A is said to be an equivalence relation if R is
reflexive, symmetric and transitive Example 2 Let T be the set of all triangles in a plane with R a relation in T given by
R = {(T1, T2) : T1 is congruent to T2}