 Solution

ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2015/discrete-mathematics-continuous-mathematics-and-probability-resit/1/a/solution

f : A \to B

f (A) = {f (a) : a \in A} \subseteq B .

The function is surjective, or onto, exactly when every

b \in B

equals

f (a)

for at least one

a \in A

, equivalently

f (A) = B

. It is injective, or one-to-one, exactly when

\forall a, a^{'} \in A, f (a) = f (a^{'}) ⟹ a = a^{'} .

Thus surjectivity concerns whether the entire codomain is reached; injectivity concerns whether distinct inputs have distinct outputs.

 New to topics? Read the docs here!