The question asks:
Define a relation R on the set of functions from R to R as follows:
(f, g) ∈ R if and only if f(x) − g(x) ≥ 0 for all x ∈ R .
Is this relation reflexive? symmetric? transitive? Is it an equivalence relation? Explain.
so far I have that the relations is reflexive because f(x)-f(x) ≥ 0: which is true
but I'm not quite sure if the relation is symmetric or transitive as I am not quite familiar.