Translate the following inference to logic notation: For all x, x_7 will cook if and only if x_7 will climb a mountain. For all x, x_14 will listen to a song if and only if x_14 is a nurse. Barbara is not listening to a song. If Joseph cooks, then Barbara is a nurse. Therefore Joseph is not climbing a mountain.
forall x: P(x) <-> Q(x). forall x: R(x) <-> S(x). ~R(a). P(b) -> S(a). Therefore ~Q(b).