Translate the following inference to logic notation: For all x, x_12 will play tennis if and only if x_12 will take a plane. There is at least one x for which if x_12 writes a letter, then x_12 is not playing tennis. For all x, x_12 is happy or x_12 is an electrician. For all x, if x_12 were an electrician, then x_12 is playing tennis. For all x, if x_12 were happy, then x_12 is taking a plane. Therefore there is at least one x for which x_12 will not write a letter.
forall x: P(x) <-> Q(x). exists x: R(x) -> ~P(x). forall x: S(x) or T(x). forall x: T(x) -> P(x). forall x: S(x) -> Q(x). Therefore exists x: ~R(x).