Translate the following inference to logic notation: There is at least one x for which x_12 is a mechanic. For all x, x_12 will make tea if and only if x_12 is an artist. For all x, x_12 is an artist and x_12 is a nurse. Therefore there is at least one x for which x_12 is a mechanic and x_12 will make tea.
exists x: P(x). forall x: Q(x) <-> R(x). forall x: R(x) and S(x). Therefore exists x: P(x) and Q(x).