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Examine whether the binary operation *...

Examine whether the binary operation `**` defined on `R` by `a**b=a b+1` is associative or not.

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We have given that the binary operation `**` defined on `R` by `a**b=a b+1`
To check association law, we have to check `(a`*`b)`*`c=a`*`(b`*`c)`
Consider, `(a`*`b)`*`c =(ab+1)`*`c`
`(a`*`b)`*`c =(ab+1)c+1`
`(a`*`b)`*`c=abc+c+1`
Again consider,
`a`*`(b`*`c)=a`*`(bc+1)`
...
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RD SHARMA-BINARY OPERATIONS-Solved Examples And Exercises
  1. Let A be a set having more than one element. Let * be a binary opera...

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  2. If the operation * is defined on the set Q of all rational numbers ...

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  3. Examine whether the binary operation ** defined on R by a**b=a b+1 i...

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  4. Let A be a set having more than one element. Let * be a binary opera...

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  5. Discuss the commutativity and associativity of the binary operation * ...

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  6. Discuss the commutativity and associativity of the binary operation * ...

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  7. Discuss the commutativity and associativity of binary operation * d...

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  8. Let * be a binary operation on N, the set of natural numbers, defined ...

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  9. Let * be a binary operation on N given by a*b=H F C(a ,\ b) for all ...

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  10. Let ** be the binary operation on N defined by a" "**" "b" "=" "Hd...

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

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

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

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

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  15. Let * be a binary operation on N defined by a*b=1. cdotmdot(a ,\ b)...

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

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

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

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  19. Let A be any set containing more than one element. Let * be a binar...

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

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