Translate the following inference to logic notation: For all x, if x_7 reads a book, then x_7 is writing a letter. For all x, if x_7 writes a letter, then x_7 is reading a book. There is at least one x for which if x_7 writes a letter, then x_7 is reading a book. Therefore there is at least one x for which if x_7 writes a letter, then x_7 is reading a book.
forall x: P(x) -> Q(x). forall x: Q(x) -> P(x). exists x: Q(x) -> P(x). Therefore exists x: Q(x) -> P(x).