(vii)Since, ‘*’ on Q defined by a * b = (a – 1)/ (b + 1) for all a, b ∈ Q
If a = 2 and b = -1 in Q,
![\[\begin{array}{*{35}{l}} a\text{ }*\text{ }b\text{ }=\text{ }\left( a\text{ }-\text{ }1 \right)/\text{ }\left( b\text{ }+\text{ }1 \right) \\ =\text{ }\left( 2\text{ }-\text{ }1 \right)/\text{ }\left( -\text{ }1\text{ }+\text{ }1 \right) \\ =\text{ }-1/0\text{ }\left[ which\text{ }is\text{ }not\text{ }defined \right] \\ \end{array}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-2f5de8196b552977b50aa145ac252c74_l3.png "Rendered by QuickLaTeX.com")
For a = 2 and b = -1
a * b does not belongs to Q
So, * is not a binary operation in Q.
Determine whether the following operation define a binary operation on the given set or not:(vii) ‘*’ on Q defined by a * b = (a – 1)/ (b + 1) for all a, b ∈ Q
Determine whether the following operation define a binary operation on the given set or not:(vii) ‘*’ on Q defined by a * b = (a – 1)/ (b + 1) for all a, b ∈ Q