Translate the following inference to logic notation: For all x, if x_10 were a doctor, then y_1 is writing a letter. For all x, if y_1 writes a letter, then x_10 is a doctor. For all x, if x_10 reads a book, then y_1 is writing a letter. For all x, x_10 is a doctor or x_10 will read a book. Therefore there is at least one x for which y_1 will write a letter.
forall x: P(x) -> Q(x). forall x: Q(x) -> P(x). forall x: R(x) -> Q(x). forall x: P(x) or R(x). Therefore exists x: Q(x).