Let P(x, y, z) be the predicate "x + y = z." (a) Simplify the statement (x)(y)(z)P(x, y, z) so that no quantifier lies within the scope of a negation. (x)(y)(z)P(x, y, z) (x)(y)(z)P(x, y, z) (x)(y)(z)P(x, y, z) (x)(y)(z)P(x, y, z) (x)(y)(z)P(x, y, z) (b) Is the statement (x)(y)(z)P(x, y, z) true in the domain of all integers? Explain why or why not. Yes. For any integers x and y, their sum z exists in the domain of integers. No. For any integers x and y, their sum z does not have to exist in the domain of integers. (c) Is the statement (x)(y)(z)P(x, y, z) true in the domain of all integers between 1 and 100? Explain why or why not. No. For example, if x = 50 and y = 70, then x + y is not in the domain. Yes. For example, if x = 25 and y = 35, then x + y is in the domain