(a) equivalence relation
f has one element ,say i.e. 1 . Two function (f and g) merging in one element . Relation will be (1,1)
(b) not reflexive
f has 2 elements , say i.e. 1,2 .But relation is (1,1) or (2,2) , but may not both
(c) not reflexive, not symmetric
distance between same element of f to g is 1 . But distance between g to f is -ve , which is not possible. So, it is not even symmetric