Translate the following inference to logic notation: For all x, x_11 will make tea or x_11 will sleep. For all x, x_11 will cook if and only if x_11 will sleep. For all x, x_11 will cook or x_11 is not a mechanic. There is at least one x for which x_11 will not make tea or x_11 is a mechanic. Therefore there is at least one x for which x_11 will cook.
forall x: P(x) or Q(x). forall x: R(x) <-> Q(x). forall x: R(x) or ~S(x). exists x: ~P(x) or S(x). Therefore exists x: R(x).