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Check commutativity and associativity
Given:
\( a * b = a – b, \quad a,b \in \mathbb{Q} \)
Commutativity:
\( a * b = a – b \)
\( b * a = b – a \)
Clearly:
\( a – b \neq b – a \)
❌ Operation is NOT commutative
Associativity:
LHS:
\( (a*b)*c = (a – b) – c = a – b – c \)
RHS:
\( a*(b*c) = a – (b – c) = a – b + c \)
Since:
\( a – b – c \neq a – b + c \)
❌ Operation is NOT associative
Conclusion:
❌ Neither commutative nor associative