Write down the negation of each of the following statements in clear and concise English....

Write down the negation of each of the following statements in clear and concise English. Do not use the expression “It is not the case that” in your answers.

(a) [BB] Either a2 > 0or a is not a real number.

(b) x is a real number and x2 +1 = 0.

(c) [BB] x = ±1.

(d) Every integer is divisible by a prime.

(e) [BB] For every real number x, there is an integer n such that h > x.

(f) There exist a, b, and c such that (ab)c ≠ a (be).

(g) [BB] There exists a planar graph that cannot be colored with at most four colors.

(h) Every Canadian is a fan of the Toronto Maple Leafs or the Montreal Canadiens.

(i) For every x > 0, x2 + y2 > 0for all y.

(j) − 2 < x < 2.

(k) [BB] For all integers a and b, there exist integers q and r such that b = qa + r.

(l) [BB] There exists an infinite set whose proper subsets are all finite.

(m) There exists a real number x such that, for every integer n, either n < x or n ≥ x + 1.

(n) If n is an integer, is not an integer.

(o) a ≤ x and a ≤ y and a ≤ z.

(p) Every vector in the plane is perpendicular to some normal.