A binary operation ⊕ ⊕ is defines on the set of all positive integers by a ⊕ ⊕ b = ab for all positive integers a, b. Which of the following properties does...

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?

Answer Details

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