Translate the following inference to logic notation: For all x, x_8 will not read a book. There is at least one x for which x_8 is a carpenter or x_8 is fast. For all x, x_8 will read a book if and only if x_8 is a carpenter. For all x, if x_8 were a carpenter, then x_8 is reading a book. Therefore there is at least one x for which x_8 is fast.
forall x: ~P(x). exists x: Q(x) or R(x). forall x: P(x) <-> Q(x). forall x: Q(x) -> P(x). Therefore exists x: R(x).