Translate the following inference to logic notation: For all x, x_7 will cook or x_7 will play tennis. For all x, x_7 will cook if and only if x_7 will listen to a song. There is at least one x for which x_7 will listen to a song or x_7 will not play tennis. Therefore there is at least one x for which x_7 will listen to a song.
forall x: P(x) or Q(x). forall x: P(x) <-> R(x). exists x: R(x) or ~Q(x). Therefore exists x: R(x).