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Q)

In the set of integers under the operation $^\ast $ defined by $a^{\ast}b=a+b-1$ the identity element is

\[\begin{array}{1 1}(1)0&(2)1\\(3)a&(4)b\end{array}\]

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A)
Let a be any element and e be the identity element.
Then, $ a *e =e * a=a$
$a *e=a$
$a+e-1=a$
$e-1=0$
$e=1$
Hence 2 is the correct answer.
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