Translate the following inference to logic notation: For all x, x_8 is a musician if and only if x_8 will play a game. For all x, x_8 will write a letter. There is at least one x for which x_8 will not write a letter or x_8 will make tea. For all x, x_8 is not a musician. Therefore there is at least one x for which x_8 will make tea.
forall x: P(x) <-> Q(x). forall x: R(x). exists x: ~R(x) or S(x). forall x: ~P(x). Therefore exists x: S(x).