Translate the following inference to logic notation: For all x, if x_7 were rich, then x_7 is a musician. There is at least one x for which x_7 is rich. For all x, x_7 will write a letter if and only if x_7 is a musician. Therefore there is at least one x for which x_7 will write a letter.
forall x: P(x) -> Q(x). exists x: P(x). forall x: R(x) <-> Q(x). Therefore exists x: R(x).