Using mathematical logic, negate the following sentence: "There exists a real number a for which a x x for every real number x."
a) For all real numbers a, there exists a real number x such that a x x > x.
b) There exists a real number a such that for all real numbers x, a x x > x.
c) For all real numbers x, there exists a real number a such that a x x > x.
d) There exists a real number x such that for all real numbers a, a x x > x.