Which of the Following Is a Negation for "For All $r s > 10 . "$

question 3

Multiple Choice

Which of the following is a negation for "For all real numbers r , there exists a number s such that $r s > 10 . "$

• A) There exists a real number r such that for all real numbers s, \(r s \ngtr 10 .\)
• B) For all real numbers r , there does not exist a number s such that \(r s > 10 .\)
• C) There exists real numbers r and s such that \(r s \ngtr 10 .\)
• D) For all real numbers r and \(s , r s \ngtr 10 .\)
• E) There exists a real number r and there does not exist a real number s such that \(r s \ngtr 10\)
• F) For all real numbers r , there exists a number s such that \(r s \ngtr 10 .\)
• G) There exists a real number r such that there does not exist a real number s with \(r s \neq 10\)