Mark each statement True or False. Justify each answer. (a) A function from A to B is a nonempty relation f ⊆ A × B such that if (a, b) ∈ f and (a, c) ∈ f , then b = c. (b) If f is a function, then...

Mark each statement True or False. Justify each answer.

(a) A function from A to B is a nonempty relation f ⊆ A × B such that if

(a, b) ∈ f and (a, c) ∈ f , then b = c.

(b) If f is a function, then the notation y = f (x) means (x, y) ∈ f.

(c) A function f : A → B is injective if for all a and a′ in A, f (a) = f (a′) implies that a = a′.

(d) If f : A → B, then A is the domain of f and B is the range of f.

(e) A function f : A → B is surjective if dom f = A.

(f ) A function f : A → B is bijective if it is one-to-one and maps A onto B.