Question 1 (10 points): Purpose: To apply basic logical inference to a non-trivial example. The questions below will address the following first-order logic knowledge base (KB). 3x Pail() A Fetch(Jack, x) Vx (3y Pail(y) A Fetch(x, y)) = Fallen(x) Vx Fallen(x) = (Vy Needed(y) = -Carries(x, y)) Carries (Jack, Water) V Carries (Jill, Water) Needed (Water) (a) (5 points) Express the above formulae in conjunctive normal form (CNF). (b) (5 points) Give a resolution proof of the query Carries(Jill, Water)use the CNF from the previous part