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Let * be a binary operation on set Q-[1]...

Let * be a binary operation on set `Q-[1]` defined by `a*b=a+b-a b` for all`a , b in Q-[1]dot` Find the identity element with respect to `*onQdot` Also, prove that every element of `Q-[1]` is invertible.

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Let `e` be the identity element.
By definition of `e`,`a xx e=a`
`a xx e=a+e−ae`
`⇒a+e−ae=a`
`⇒e(1−a)=0`
`⇒e=0` (Since a is not equal to 1)
`⇒e=0 in G`
Identify element is `Q` ...
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RD SHARMA-BINARY OPERATIONS-Solved Examples And Exercises
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  2. On Q, the set of all rational numbers, a binary operation * is defined...

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  3. Let * be a binary operation on set Q-[1] defined by a*b=a+b-a b for al...

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  4. Show that the binary operation * on A=R-{-1} defined as a*b=a+b+a b fo...

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  5. Let '*' be a binary operation on Q0 (set of all non-zero rational numb...

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  6. Let '*' be a binary operation on Q0 (set of all non-zero rational numb...

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  9. Define a binary operation * on the set A={0,1,2,3,4,5} given by a*b=a ...

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  11. Let X be a non-empty set and let * be a binary operation on P(X) (t...

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  12. Let X be a nonempty set and *be a binary operation on P(X), the power ...

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  13. Let X be a non-empty set and let * be a binary operation on P\ (X) ...

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  14. Let X be a non-empty set and let * be a binary operation on P\ (X) ...

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

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

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  17. Let A=Nuu{0}xxNuu{0} and let * be a binary operation on A defined b...

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  18. Let A=Nuu{0}xxNuu{0} and let * be a binary operation on A defined b...

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

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  20. Let A=NxxN , and let * be a binary operation on A defined by (a ,\ ...

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