Translate the following inference to logic notation: If Thomas were sad, then Patricia is sleeping. Patricia is not a soldier. For all x, x_14 is a soldier if and only if x_14 will sleep. For all x, x_7 is sad if and only if x_7 will write a letter. Therefore Thomas is not writing a letter.
P(a) -> Q(b). ~R(b). forall x: R(x) <-> Q(x). forall x: P(x) <-> S(x). Therefore ~S(a).