Translate the following inference to logic notation: For all x, if x climbs a mountain, then x is reading a book. For all x, if x reads a book, then x is writing a letter. For all x, x will climb a mountain if and only if x will write a letter. Therefore if Richard climbs a mountain, then Richard is writing a letter.
forall x: P(x) -> Q(x). forall x: Q(x) -> R(x). forall x: P(x) <-> R(x). Therefore P(a) -> R(a).