- a ∗ b = a – b
- a ∗ b = a2 + b2
Arrangement:
(i) a ∗ b = a – b
a ∗ b = a – b = – (b – a) = – b * c ≠ b * a (Not commutative)
(a * b) * c = (a – b) * c = (a – (b – c) = a – b + c ≠ a * (b *c) (Not cooperative)
(ii) a ∗ b = a2 + b2
a ∗ b = a2 + b2 = b2 + a2 = b * a (activity is commutative) Check for cooperative:
(a * b) * c = (a2 + b2) * c2 = (a2 + b2) + c2 a * (b *c) = a * (b2 + c2 ) = a2 * (b2 + c2 )2 (a * b) * c ≠ a * (b *c) (Not cooperative)