A B A B A B A B f A B f : A → B f (a) B f a ∈ A f a a f R C f : A → B A A f (A ) A B B f ( − 1)(B ) A B f (A ) = {f (a) : a ∈ A } f −1 (B ) = {a ∈ A : f (a) ∈ B } f (A ) A f −1 (B ) B f (A) f f : A → B A × B {(a, f (a)) : a ∈ A} f f : A → B g : A → B f = g f (a) = g (a) a ∈ A f = g f = g a ∈ A f (a) = g (a) → x ∈ A f : A → B x → f (x)