Translate the following inference to logic notation: For all x, if x_2 were an office clerk, then x_2 is cooking. For all x, x_2 will cook if and only if x_2 will make tea. If Sarah makes tea, then Sarah is an office clerk. Therefore Sarah is an office clerk if and only if Sarah is making tea.
forall x: P(x) -> Q(x). forall x: Q(x) <-> R(x). R(a) -> P(a). Therefore P(a) <-> R(a).