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Question
Determine whether the following operation define a binary operation on the given set or not :
\[' * ' \text{on Q defined by } a * b = \frac{a - 1}{b + 1} \text{for all a, b} \in Q .\]
Solution
If a = 2 and b = \[-\] 1 in Q,
\[ = \frac{2 - 1}{- 1 + 1}\]
\[ = \frac{1}{0} \left[ \text{ which is not defined } \right]\]
\[\Rightarrow \text{ Fora} = 2 \text{ and }b = - 1, \]
\[a * b \not\in Q\]
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