Let P(n, x, y, z) be the predicate "xn + yn = zn." (a) Write the following statement in predicate logic, using positive integers as the domain. For every positive integer n, there exist positive integers x, y, and z such that xn + yn = zn. (3n)(vx)(vy)(vz)P(n, x, y, z) (3)(3x)(3)(3)P(n, x, y, z) (3)(3x)(3)(v)P(n, x, y, z) (vn)(vx)(vy)(vz)P(n, x, y, z) (vn)(3x)(3)(az)P(n, x, y, z) (b) Formally negate your predicate logic statement from part (a). Simplify so that no quantifier lies within the scope of a negation. (vn)(vx)(vy) (vz)(P(n, x, y, z)) (vn)(3x)(3)(3)(P(n, x, y, z)) (3)(vx)(vy)(vz)(-P(n, x, y, z)) (vn)(vx)(vy)(3)(P(n, x, y, z)) (3)(3x)(3)(3)(-P(n, x, y, z)) (c) In order to produce a counterexample to the statement in part (a), what, specifically, would you have to find? You would have to find a positive integer ? such that the equation xn + yn = zn has ---Select--- for any positive integers ---Select---.