Translate the following inference to logic notation: For all x, x_6 will write a letter. For all x, if x_6 cooks, then x_6 is listening to a song. For all x, x_6 is bored. For all x, x_6 will cook. Therefore for all x, x_6 is bored and x_6 will write a letter.
forall x: P(x). forall x: Q(x) -> R(x). forall x: S(x). forall x: Q(x). Therefore forall x: S(x) and P(x).