Translate the following inference to logic notation: Barbara is a writer if and only if it is sunny. Joseph is not a lawyer. For all x, x is a lawyer if and only if x will read a book. It is sunny if and only if Joseph is reading a book. Therefore Barbara is not a writer.
p <-> q. ~P(a). forall x: P(x) <-> Q(x). q <-> Q(a). Therefore ~p.