Translate the following inference to logic notation: For all x, if x_8 writes a letter, then x_8 is running. There is at least one x for which x_8 will make tea if and only if x_8 will write a letter. For all x, x_8 is not a mechanic. For all x, x_8 will go running if and only if x_8 is a mechanic. Therefore there is at least one x for which x_8 will not make tea.
forall x: P(x) -> Q(x). exists x: R(x) <-> P(x). forall x: ~S(x). forall x: Q(x) <-> S(x). Therefore exists x: ~R(x).