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Let A be a non-empty set and S be the se...

Let `A` be a non-empty set and `S` be the set of all functions from `A` to itself. Prove that the composition of functions `'o'` is a non-commutative binary operation on `Sdot` Also, prove that `'o'` is an associative binary operation on `Sdot`

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RD SHARMA ENGLISH-BINARY OPERATIONS-All Questions
  1. Let ** be the binary operation on N defined by a" "**" "b" "=" "Hd...

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  2. Consider the binary operations*: RxxR->R and o: RxxR->R defined as a...

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  3. Let A be a non-empty set and S be the set of all functions from A t...

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  4. Let A=NxNa n d^(prime)*' be a binaryoperation on A defined by (a , b)*...

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  5. Let A be a set having more than one element. Let * be a binary oper...

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  6. Let * be a binary operation on N defined by a*b=LCM(a ,\ b) for all ...

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

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  8. Determine whether * on N defined by a * b=1 for all a ,\ b in N is ...

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  9. Determine whether * on Q defined by a*b=(a+b)/2 for all a ,\ b in Q i...

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  10. Let A be any set containing more than one element. Let * be a binary...

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  11. Check the commutativity of * on Z defined by a*b=a+b+a b for all a ,\ ...

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  12. Check the commutativity of * on N defined by a*b=2^(a b) for all a ,\ ...

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  13. Check the commutativity of * on Q defined by a*b=a-b for all a ,\ b in...

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  14. Check the commutativity of O on Q defined by a\ \ b=a^2+b^2 for all a ...

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  15. Check the commutativity and associativity of * on Q defined by a * ...

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  16. Check the commutativity of * on Q defined by a*b=a b^2 for all a ,\ b ...

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  17. Check the commutativity of * on Q defined by a*b=a+a b for all a ,\ b ...

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  18. Check the commutativity and associativity of * on R defined by a*b=...

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  19. Check the commutativity of * on Q defined by a*b=(a-b)^2 for all a ,\ ...

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  20. Check the commutativity and associativity of * on Q defined by a*b=...

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