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Determine associativity and commutativity
Given:
\( a * b = 1 \quad \forall \, a,b \in \mathbb{N} \)
Commutativity:
\( a * b = 1 = b * a \)
✔ Operation is commutative
Associativity:
Check:
\( (a*b)*c = 1*c = 1 \)
\( a*(b*c) = a*1 = 1 \)
✔ Operation is associative
Conclusion:
✔ The operation is both commutative and associative.