This is question about partial ordered sets and function.
Let ⟨A,≼A⟩ be a poset, B a set, and f : B → A a function. Let ≼B ⊆ B × B be the relation defined by, for all x,y ∈ B, x ≼B y if and only if f(x) ≼A f(y).
(a) Show that if ≼B is a partial order then f is injective.
(b) Show that if f is injective then ≼B is a partial order.
