Translate the following inference to logic notation: For all x, x will take a plane or x is a soldier. For all x, x is fast or x will not take a plane. For all x, x is a soldier if and only if x is fast. Therefore for all x, x is fast.
forall x: P(x) or Q(x). forall x: R(x) or ~P(x). forall x: Q(x) <-> R(x). Therefore forall x: R(x).