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Let 'O' Be a Binary Operation on the Set Q0 of All Non-zero Rational Numbers Defined by a O B = a B 2 , for All A, B ∈ Q 0 : Find the Identity Element in Q0. - Mathematics

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प्रश्न

Let 'o' be a binary operation on the set Q0 of all non-zero rational numbers defined by \[a o b = \frac{ab}{2}, \text{ for all a, b } \in Q_0\] :

 Find the identity element in Q0.

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उत्तर

Let e be the identity element in Qo with respect to * such that

\[a o e = a = e o a, \forall a \in Q_0 \] 
\[a o e = a \text{ and }e o a = a, \forall a \in Q_0 \] 
\[ \Rightarrow \frac{ae}{2} = a \text{ and }\frac{ea}{2} = a, \forall a \in Q_0 \] 
\[e = 2 \in Q_0 , \forall a \in Q_0\]

Thus, 2 is the identity element in Qo with respect to o.

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पाठ 3: Binary Operations - Exercise 3.4 [पृष्ठ २५]

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आरडी शर्मा Mathematics [English] Class 12
पाठ 3 Binary Operations
Exercise 3.4 | Q 5.2 | पृष्ठ २५

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