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Find the identity element in the set of all rational numbers except -1 with respect to * defined by `a*b=a+b+a b` .

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Let `e` be the identity element.
Then according to the definition of the identity element we get, `a∗e=e∗a=a` for all `a in Q−{−1}`.
Then we have, `a+e+ae=a` or, `e(a+1)=0`
Since `a != ...
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  18. Let X be a non-empty set and let * be a binary operation on P\ (X) ...

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  19. Let A=QxxQ and let ** be a binary operation on A defined by (a ,\ b)...

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