Let * be a binary operation on the set Q of rational numbers as follow

1.	Let * be a binary operation on the set Q of rational numbers as follows. Find which of the binary operations are commutative and which are associative. a * b = a2 + b2
Answer» a, b ∈ Q ⇒ a * b = a² + b² = b² + a² = b * a hence * is commutative (a * b) * c = (a² + b²) * c² = (a² + b²)² + c² a(b c) = a* (b²+ c²) = a² + (b² + c²)² hence * is not associative

Let * be a binary operation on the set Q of rational numbers as follows. Find which of the binary operations are commutative and which are associative. a * b = a2 + b2

Answer»

a, b ∈ Q ⇒ a * b = a² + b²

= b² + a² = b * a

hence * is commutative

(a * b) * c = (a² + b²) * c²

= (a² + b²)² + c²

a*(b * c) = a* (b²+ c²)

= a² + (b² + c²)²

hence * is not associative