Express the negations of each of the following statements using quantifier notation as fully as possible, but without using the negation symbol (you may use symbols such as X, #, etc.): a) x is an upper bound for S. (Here, S is a subset of R and x is a real number.) b) is a prime. (Here, is an integer greater than 1.) c) u is rational. (Here, u is a real number.) d) d is the GCD of a and b. (Here, a, b, and d are positive integers.) (Careful!) e) R is a function from A to B. (Here, R is a subset of A X B.) f) f is strictly increasing. (Here, f is a function from R to R.) g) f is injective. (Here, f is a function from A to B.) h) f is surjective. (Here, f is a function from A to B.) i) S is an interval. (Here, S is a subset of R. Use the definition of "interval" in Exer- cise 15)

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