Translate the following inference to logic notation: For all x, x will read a book or x is a politician. For all x, x is a doctor if and only if x will read a book. For all x, x will not take a plane. There is at least one x for which x is a doctor if and only if x will take a plane. Therefore there is at least one x for which x is a politician.
forall x: P(x) or Q(x). forall x: R(x) <-> P(x). forall x: ~S(x). exists x: R(x) <-> S(x). Therefore exists x: Q(x).