The negation of the statement "For all real numbers x and y, x + y = y + x" is

Question

The negation of the statement "For all real numbers x and y, x + y = y + x" is (A) For all real numbers x and y, x + y ≠ y + x (B) For some real numbers x and y, x+y = y+x (C) For some real number x and y, x + y ≠ y + x (D) for some real numbers x and y, x-y=y-x

Tardigrade Admin · Accepted Answer

Negation: For some real numbers x and y, x + y ≠ y + x.

Q. The negation of the statement "For all real numbers x and y, x + y = y + x" is

For all real numbers x and y, x + y $\neq =$ y + x

For some real numbers x and y, x+y = y+x

For some real number x and y, x + y $\neq =$ y + x

for some real numbers x and y, x-y=y-x

Negation: For some real numbers $x$ and $y, x + y \neq = y + x$ .

Q. The negation of the statement "For all real numbers x and y, x + y = y + x" is

For all real numbers x and y, x + y = y + x

For some real numbers x and y, x+y = y+x

For some real number x and y, x + y = y + x

for some real numbers x and y, x-y=y-x

Negation: For some real numbers x and y,x+y=y+x.

For all real numbers x and y, x + y $\neq =$ y + x

For some real number x and y, x + y $\neq =$ y + x

Negation: For some real numbers $x$ and $y, x + y \neq = y + x$ .