Prove that the following argument is valid. Use only the rules of inference (including the instantiation and generalization rules) and the logical equivalences (as both were presented in class). Be sure to number each line in your proof and label which rules you used to derive it (if it a premise state that it is a premise) (6 marks) Vz-A (x) B (x) 3x-C-A (x) (x)) Vx -D(x)-C(x) vx D(x)E (x) . 3x E(x) For every integer n, prove that 3n 5 is even if and only if n is odd. (4 marks) The ceiling of a real number x, denoted by [x], is the unique integer that satisfies the inequality: [x]-1