Translate the following inference to logic notation: For all x, if x_7 writes a letter, then x_7 is not making tea. There is at least one x for which if x_7 were sad, then x_7 is making tea. For all x, if x_7 were a carpenter, then x_7 is making tea. For all x, x_7 is sad or x_7 is a carpenter. Therefore there is at least one x for which x_7 will not write a letter.
forall x: P(x) -> ~Q(x). exists x: R(x) -> Q(x). forall x: S(x) -> Q(x). forall x: R(x) or S(x). Therefore exists x: ~P(x).