A binary operation \(\oplus\) is defines on the set of all positive integers by a \(\oplus\) b = ab for all positive integers a, b. Which of the following properties does NOT hold?
A. closure B. identity C. positive D. inverse
Correct Answer: D
Explanation
a \(\oplus\) b = ab The set of all national rules Q, is closed under the operations, additions, subtraction, multiplication and division. Since a \(\oplus\) b = ab; b \(\oplus\) a = ba = ab The number 1 is the identity element under multiplication
