Translate the following inference to logic notation: For all x, if z were an electrician, then z is writing a letter. For all x, z is an electrician if and only if z is a musician. For all x, if z were happy, then z is a musician. For all x, z is fast if and only if z is a musician. For all x, z is happy or z is fast. Therefore for all x, z will write a letter.
forall x: P(x) -> Q(x). forall x: P(x) <-> R(x). forall x: S(x) -> R(x). forall x: T(x) <-> R(x). forall x: S(x) or T(x). Therefore forall x: Q(x).