Translate the following inference to logic notation: For all x, if x_7 plays squash, then x_7 is listening to a song. For all x, x_7 is a carpenter or x_7 will read a book. There is at least one x for which if x_7 reads a book, then x_7 is listening to a song. For all x, x_7 is a carpenter if and only if x_7 will play squash. Therefore there is at least one x for which x_7 will listen to a song.
forall x: P(x) -> Q(x). forall x: R(x) or S(x). exists x: S(x) -> Q(x). forall x: R(x) <-> P(x). Therefore exists x: Q(x).