Translate the following inference to logic notation: There is at least one x for which x_10 will play a game or x_10 will make tea. For all x, x_10 is a mechanic if and only if x_10 is an astronaut. For all x, x_10 will make tea if and only if x_10 is a mechanic. For all x, x_10 will not play a game or x_10 is an astronaut. Therefore there is at least one x for which x_10 is a mechanic.
exists x: P(x) or Q(x). forall x: R(x) <-> S(x). forall x: Q(x) <-> R(x). forall x: ~P(x) or S(x). Therefore exists x: R(x).