Which of the following is a negation for Given any real numbers a and b; if a an

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.

Please explain your reasoning for your answer.

Explanation / Answer

negation of given statement is E

statement is saying for all a,b belongs to R if a and b belongs to Q then a/b belongs to Q

its negation is there exist a,b belongs to R st a and b belongs to Q and a/b doesnot belongs to Q

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