Translate the following inference to logic notation: For all x, if y_4 were a musician, then y_4 is listening to a song. For all x, y_4 is a musician. For all x, y_4 is a mechanic. There is at least one x for which y_4 is bored. Therefore there is at least one x for which y_4 is a mechanic and y_4 is bored.
forall x: P(x) -> Q(x). forall x: P(x). forall x: R(x). exists x: S(x). Therefore exists x: R(x) and S(x).