Let * be defined on the set of non-zero rational numbers Q by a * b = a/b. Then * is:

Let * be defined on the set of non-zero rational numbers Q by a * b = a/b. Then * is:

• A. Commutative and associative
• B. Commutative but not associative
• C. Associative but not commutative
• D. Neither commutative nor associative

Answer: D) Neither commutative nor associative

Explanation: a * b = a/b, but b * a = b/a, so not commutative. Also, (a * b) * c = (a/b)/c = a/(bc), whereas a * (b * c) = a/(b/c) = (ac)/b. Hence, not associative.