Translate the following inference to logic notation: For all x, x_8 will not listen to a song. For all x, x_8 is a musician if and only if x_8 is sad. For all x, x_8 will write a letter or x_8 is a musician. There is at least one x for which x_8 will not write a letter or x_8 is bored. For all x, if x_8 were sad, then x_8 is listening to a song. Therefore there is at least one x for which x_8 is bored.
forall x: ~P(x). forall x: Q(x) <-> R(x). forall x: S(x) or Q(x). exists x: ~S(x) or T(x). forall x: R(x) -> P(x). Therefore exists x: T(x).