Translate the following inference to logic notation: For all x, if x_12 writes a letter, then x_12 is climbing a mountain. There is at least one x for which x_12 will write a letter or x_12 is sad. For all x, x_12 is sad if and only if x_12 will climb a mountain. For all x, x_12 is an electrician. Therefore there is at least one x for which x_12 is an electrician and x_12 will climb a mountain.
forall x: P(x) -> Q(x). exists x: P(x) or R(x). forall x: R(x) <-> Q(x). forall x: S(x). Therefore exists x: S(x) and Q(x).