Which of the following is a negation for "There exists a real number x such that for all real Numbers y, xy y."
A) There exists a real number x such that for all real numbers $y , x y \leq y$
B) There exists a real number y such that for all real numbers $x , x y \leq y .$
C) There exist real numbers x and y such that $x y \leq y$
D) For all real numbers x there exists a real number y such that
$x y \leq y \text {. }$
E) For all real numbers y there exists a real number x such that $x y \leq y \text {. }$
F) For all real numbers x and $y , x y \leq y .$

Question

Which of the following is a negation for "There exists a real number x such that for all real Numbers y, xy > y." 
A) There exists a real number  x  such that for all real numbers $y , x y \leq y$
B) There exists a real number  y  such that for all real numbers $x , x y \leq y .$
C) There exist real numbers  x  and  y  such that $x y \leq y$
D) For all real numbers  x  there exists a real number  y  such that 
$x y \leq y \text {. }$
E) For all real numbers  y  there exists a real number  x  such that $x y \leq y \text {. }$
F) For all real numbers  x  and $y , x y \leq y .$

Quizplus · Accepted Answer

The negation of "There exists a real number x such that for all real numbers y, xy > y" is "For all real numbers x there exists a real number y such that xy ≤ y." This is because negation involves switching "There exists" to "For all" and changing the inequality from ">" to "≤".

Which of the Following Is a Negation for "There Exists y,xy≤yy , x y \leq yy,xy≤y

Which of the Following Is a Negation for "There Exists $y , x y \leq y$