Translate the following inference to logic notation: For all x, y is a doctor if and only if y is a soldier. For all x, y will work if and only if y will read a book. There is at least one x for which y is not a doctor. For all x, y is a soldier if and only if y will work. Therefore there is at least one x for which y will not read a book.
forall x: P(x) <-> Q(x). forall x: R(x) <-> S(x). exists x: ~P(x). forall x: Q(x) <-> R(x). Therefore exists x: ~S(x).