Translate the following inference to logic notation: For all x, x_1 will write a letter. For all x, x_1 is fast. For all x, if x_1 writes a letter, then x_1 is making tea. Therefore for all x, x_1 will make tea and x_1 is fast.
forall x: P(x). forall x: Q(x). forall x: P(x) -> R(x). Therefore forall x: R(x) and Q(x).