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Consider the binary operation ast defi...

Consider the binary operation `ast` defined on `Q-{1}` by the rule `a ast b=a+b-a b` for all `a ,\ b in Q-{1}` . The identity element in `Q-{1}` is

A

(a) `0`

B

(b) `1`

C

(c) `frac{1}{2}`

D

(d) `-1`

Text Solution

Verified by Experts

The correct Answer is:
(a) `0`
Let `e=` identity element
`a ast e = e ast a=a`
`a ast b=a+b-ab`
`a ast e=a+e-ae`
`a=a+e-ae`
`e(1-a)=0`
`1-a ne 0`
`e=0`
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RD SHARMA-BINARY OPERATIONS-Solved Examples And Exercises
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  2. If the binary operation o. is defined on the set Q^+ of all positive r...

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  3. Let * be a binary operation defined on set Q-{1} by the rule a*b=a+b...

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  4. Which of the following is true? * defined by a*b=(a+b)/2 is a binar...

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  5. The binary operation * defined on N by a*b=a+b+a b for all a ,\ b i...

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  6. If a binary operation * is defined by a*b=a^2+b^2+a b+1 , then (2*3...

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  7. Let * be a binary operation on R defined by a*b=a b+1 . Then, * is ...

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  8. Subtraction of integers is

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  9. The law a+b=b+a is called

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  10. An operation * is defined on the set Z of non-zero integers by a*b=a/...

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  11. On Z an operation * is defined by a * b=a^2+b^2 for all a ,\ b in Z...

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  12. A binary operation ast on Z defined by a ast b=3a+b for all a ,\ b i...

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  13. Letastbe a binary operation on N defined by a ast b=a+b+10 for all a...

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  14. Consider the binary operation ast defined on Q-{1} by the rule a ast...

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  15. For the binary operation ast defined on R-{-1} by the rule a ast b=a...

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  16. For the multiplication of matrices as a binary operation on the set ...

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  17. On the set Q^+ of all positive rational numbers a binary operation *...

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  18. Let ast be a binary operation defined on Q^+ by the rule a ast b=(a...

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  19. The number of binary operations that can be defined on a set of 2 el...

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  20. The number of commutative binary operations that can be defined on a...

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