Discussion
Which of the following is not true for rational numbers ?
Answer: A
Rational numbers are not closed under division.
A set is closed under an operation if the result of the operation on any two members is again a member. For rational numbers \(a\) and \(b\), \(a + b\), \(a - b\) and \(a \times b\) are always rational.
Division fails in one case: \(a \div 0\) is not defined, so it is not a rational number. Because of that single exception, rational numbers are not closed under division, although the non-zero rationals are. Addition, subtraction and multiplication are all closed, so those statements are true.
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