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Question
Let S be the set of all rational numbers except 1 and * be defined on S by a * b = a + b \[-\] ab, for all a, b \[\in\] S:
Prove that * is a binary operation on S ?
Solution
We have,
S = R \[-\] {1} and * is defined on S as a * b = a + b \[-\]ab, for all a, b \[\in\] S
It is seen that for each a, b \[\in\] S, there is a unique element a + b \[-\] ab in S
This means that * carries each pair (a, b) to a unique element a * b = a + b \[-\] ab in S
So, * is a binary operation on S
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