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: Option 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