Translate the following inference to logic notation: For all x, x_1 will write a letter if and only if x_1 is a carpenter. There is at least one x for which if x_1 were a carpenter, then x_1 is playing squash. For all x, if x_1 plays squash, then x_1 is a bartender. Therefore there is at least one x for which if x_1 writes a letter, then x_1 is a bartender.
forall x: P(x) <-> Q(x). exists x: Q(x) -> R(x). forall x: R(x) -> S(x). Therefore exists x: P(x) -> S(x).