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

Correct answer is D

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

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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?