Translate the following inference to logic notation: For all x, x_7 is a politician if and only if x_7 is a doctor. If William were a taxi driver, then Elisabeth is sleeping. Elisabeth is not sleeping. If John were a doctor, then William is a taxi driver. Therefore John is not a politician.
forall x: P(x) <-> Q(x). p -> q. ~q. Q(a) -> p. Therefore ~P(a).