Which of the following is a negation for "Given any real numbers a and b , if a and b are rational then a / b is rational."
A) There exist real numbers a and b such that a and b are not rational and a / b is not rational.
B) Given any real numbers a and b , if a and b are not rational then a / b is not rational.
C) There exist real numbers a and b such that a and b are not rational and a / b is rational.
D) Given any real numbers a and b , if a and b are rational then a / b is not rational.
E) There exist real numbers a and b such that a and b are rational and a / b is not rational.
F) Given any real numbers a and b , if a and b are not rational then a / b is rational.

Question

Which of the following is a negation for "Given any real numbers  a  and  b , if  a  and  b  are rational then  a / b  is rational."
A) There exist real numbers  a  and  b  such that  a  and  b  are not rational and  a / b  is not rational.
B) Given any real numbers  a  and  b , if  a  and  b  are not rational then  a / b  is not rational.
C) There exist real numbers  a  and  b  such that  a  and  b  are not rational and  a / b  is rational.
D) Given any real numbers  a  and  b , if  a  and  b  are rational then  a / b  is not rational.
E) There exist real numbers  a  and  b  such that  a  and  b  are rational and  a / b  is not rational.
F) Given any real numbers  a  and  b , if  a  and  b  are not rational then  a / b  is rational.

Quizplus · Accepted Answer

The correct negation of the statement involves finding a specific counterexample where $a$ and $b$ are rational, but $a/b$ is not rational. This directly contradicts the original statement's claim that for any rational $a$ and $b$, $a/b$ will also be rational.

Which of the Following Is a Negation for "Given Any