Translate the following inference to logic notation: For all x, z will read a book if and only if z is a mechanic. For all x, z is a mechanic if and only if z will read a book. Therefore if Richard were a mechanic, then Richard is reading a book.
forall x: P(x) <-> Q(x). forall x: Q(x) <-> P(x). Therefore Q(a) -> P(a).