Let * be a binary operation on N given by a * b = a² + b². Then * is:
Let * be a binary operation on N given by a * b = a² + b². Then * is:
- A. Commutative and associative
- B. Associative but not commutative
- C. Commutative but not associative
- D. Neither commutative nor associative
Answer: C) Commutative but not associative
Explanation: a * b = a² + b² = b² + a² = b * a, so it is commutative. However, (a * b) * c = (a² + b²) * c = (a² + b²)² + c², whereas a * (b * c) = a² + (b² + c²)². They are not equal, so not associative.
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