I need the complete working solutions and accurate answers to this question. Thanks

Problem 1. (15 points) (i) For2(P(z) 0(x)), distributing the quantifier over the operator results in dieP(x) A3nQ(x). Are the two expressions equivalent? If they are, give a proof. If they are not, provide a counterexample and explain any direction of the implication that does not hold. Any counterexample needs to have a universe of size at least 100. (ii) Express the negation of 3dyR(x,y) ,s(x,y) so that all negation symbols immediately precede predicates. Show your work