- Is ∗ both associative and commutative?
- Is ∗ commutative but not associative?
- Is ∗ associative but not commutative?
- Is ∗ neither commutative nor associative?
solution:
A two fold activity ∗ on N characterized as a ∗ b = a3 + b3 ,
Likewise, a ∗ b = a3 + b3 = b3 + a3 = b * a The activity * is commutative.
Once more, (a ∗ b)*c = (a3 + b3 ) * c = ( a3 + b3 )3 + c3 a * (b * c) = a * (b3 + c3 ) = a3 + (b3 + c3 )3
(a ∗ b)*c ≠ a * (b * c)
The activity * isn’t affiliated. Along these lines, alternative (2) is right.