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Let '*' be a binary operation on N given...

Let `'*'` be a binary operation on N given by `a*b=LdotCdotMdot(a , b)` for all `a , b in Ndot` Find `5*7,20*16` (ii) Is * commutative? Is * associative? Find the identity element in N Which element of N are invertible? Find them.

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(i) `5 * 7 =` L.C.M. of `5` and `7 = 35`
` 20 * 16 =` L.C.M. of `20 `and `16 = 80`
(ii) Let `a,b, in N`
` a* b =` L.C.M. of `a` and `b =` L.C.M. of `b` and `a =b*a`
Operation * is commutative .
(iii) Let `a,b,c in N`
`a* ( b* c) = a*` (L.C.M of `b` and `c`) =L.C.M of `a,b` and `c `
`=`(L.C.M of `a` and `b` ) `*c` ...
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RD SHARMA-BINARY OPERATIONS-Solved Examples And Exercises
  1. Let '*' be a binary operation on Q0 (set of all non-zero rational numb...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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  16. Show that the number of binary operations on {1," "2} having 1 as iden...

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  17. Determine the total number of binary operations on the set S={1,\ 2...

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  18. Let * be a binary operation on Z defined by a*b=a+b-4 for all a ,\ ...

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  19. Let * be a binary operation on Z defined by a*b=a+b-4 for all a ,\ ...

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

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