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?
- closure
- identity
- positive
-
inverse
The correct answer is: D
Explanation
a \(\oplus\) b = abThe 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