Translate the following inference to logic notation: It is raining. John is not a doctor. If John doesn't write a letter, then Elisabeth is making tea. For all x, x_20 will write a letter if and only if x_20 is a doctor. Therefore it is raining and Elisabeth is making tea.
p. ~P(a). ~Q(a) -> q. forall x: Q(x) <-> P(x). Therefore p and q.