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Find the identity element in the set ...

Find the identity element in the set `I^+` of all positive integers defined by `a*b=a+b` for all `a ,\ b in I^+` .

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Let e be the identity element in `I ^+` with respect to `∗` such that
`⇒ a∗e=a=e∗a`, for all `a in I ^+`
`⇒ a∗e=a and e∗a=a`, for all `a in I ^+` ...
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RD SHARMA-BINARY OPERATIONS-Solved Examples And Exercises
  1. If * is defined on the set R of all real numbers by a*b=sqrt(a^2+b^2) ...

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  2. Let S be a non-empty set and P(s) be the power set of set S. Find the ...

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  3. Find the identity element in the set I^+ of all positive integer...

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  4. Find the identity element in the set of all rational numbers except ...

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  5. If the binary operation * on the set Z is defined by a*b=a+b-5, then ...

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  6. On the set Z of integers, if the binary operation * is defined by a...

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  7. On Q, the set of all rational numbers, a binary operation * is defined...

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

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

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

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

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  12. Let * be a binary operation on N given by a*b=LdotCdotM(a ,\ b) for...

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  13. Let '*' be a binary operation on N given by a*b=LdotCdotMdot(a , b) fo...

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

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  15. On the set M=A(x)={[xxxx]: x in R}of2x2 matrices, find the identity ...

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

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

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

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

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