Translate the following inference to logic notation: For all x, if y listens to a song, then y is reading a book. There is at least one x for which y will climb a mountain if and only if y will read a book. For all x, y will climb a mountain or y is a cashier. For all x, if y were a cashier, then y is listening to a song. Therefore there is at least one x for which y will read a book.
forall x: P(x) -> Q(x). exists x: R(x) <-> Q(x). forall x: R(x) or S(x). forall x: S(x) -> P(x). Therefore exists x: Q(x).