Problem

Give a useful denial of each statement. (a) x is a positive integer. (Assume th...

Give a useful denial of each statement.

(a) x is a positive integer. (Assume that x is some fixed integer.)

(b) Cleveland will win the first game or the second game.

(c) 5 ≥ 3.

(d) 641,371 is a composite integer.

(e) Roses are red and violets are blue.

(f) T is not bounded or T is compact. (Assume that T is a fixed object.)

(g) M is odd and one-to-one. (Assume that M is some fixed function.)

(h) The function f has positive first and second derivatives at x0(Assume that f is a fixed function and x0 is a fixed real number.)

(i) The function g has a relative maximum at x = 2 or x = 4 and a relative minimum at x = 3 (Assume that g is a fixed function.)

(j) Neither z < s nor z t is true. (Assume that z, s, and t are fixed real numbers.)

(k) R is transitive but not reflexive. (Assume that R is a fixed object.)

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Solutions For Problems in Chapter 1.1