Translate the following inference to logic notation: For all x, x_17 will cook if and only if x_17 is fast. There is at least one x for which if x_17 were poor, then x_17 is driving a car. For all x, x_17 is fast if and only if x_17 is poor. For all x, x_17 will make tea if and only if x_17 will cook. For all x, x_17 will not drive a car. Therefore there is at least one x for which x_17 will not make tea.
forall x: P(x) <-> Q(x). exists x: R(x) -> S(x). forall x: Q(x) <-> R(x). forall x: T(x) <-> P(x). forall x: ~S(x). Therefore exists x: ~T(x).