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Show that the operation is commutative
Given:
\( a \circ b = a + b – ab, \quad a,b \in \mathbb{Q} \setminus \{-1\} \)
Proof:
Compute:
\( a \circ b = a + b – ab \)
\( b \circ a = b + a – ba \)
Since:
\( b + a = a + b \quad \text{and} \quad ba = ab \)
We get:
\( b \circ a = a + b – ab \)
\( \Rightarrow a \circ b = b \circ a \)
Conclusion:
✔ Therefore, the operation is commutative on \( \mathbb{Q} \setminus \{-1\} \).