22. 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 \(\forall\), \(\neq\), etc.):
a) x is an upper bound for S. (Here, S is a subset of R and x is a real number.)
b) \(t\) is a prime. (Here, \(t\) 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 \(A \times B\).)
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 Exercise
15.)