A binary operation \(\oplus\) is defines on the set of all positive integers by a...

JAMB 1994

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

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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

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