Given A = {0, 1, 2, 3} and a relation R on A defined as

F = {(0, 0) (0, 1), (0, 3), (1, 0), (1, 1), (2, 2), (3, 0), (3, 3)}

A relation is an equivalence relation if and only if it is reflexive, symmetric and transitive:

(i) The set contains (0,0),(1,1),(2,2),(3,3):

Hence (a,a) ∈ R → R is reflexive.

(ii)The set also contains (0,1),(1,0) and (0,3),(3,0)

Hence (a,b) ∈ R and (b,a) ∈ R → R is symmetric.

(ii) The set also contains (0,0),(0,1) and (0,0),(0,3)

Hence (a,b) ∈ R, (b,c) ∈ R and (a,c) ∈ R → R is transitive.

Hence R is reflexive,symmetric and transitive.