Translate the following inference to logic notation: For all x, if x reads a book, then x is not writing a letter. There is at least one x for which x will write a letter. For all x, if x reads a book, then x is a politician. For all x, if x were a politician, then x is reading a book. Therefore there is at least one x for which x is not a politician.
forall x: P(x) -> ~Q(x). exists x: Q(x). forall x: P(x) -> R(x). forall x: R(x) -> P(x). Therefore exists x: ~R(x).