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
Verified Correct Answer: D.
Step-by-Step Mathematical Solution
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
Source: Myschool Past Questions Archive (Record #31016)