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Let S be the set of all rational numbe...

Let `S` be the set of all rational numbers of the form `m/n` , where `m in Z` and `n=1,\ 2,\ 3.` Prove that * on `S` defined by `a`*`b=a b` is not a binary operation.

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Let `S={m/n:m inZ,n` takes the values`1,2,3}`
Let `x=1/2`,`y=1/3` where `m=1`,`n=2,3`
`implies xy=1/2xx1/3=1/6` where `6!inS`
Hence * is not a binary operation on S.
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RD SHARMA-BINARY OPERATIONS-Solved Examples And Exercises
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  2. Prove that the operation * on the set M={[(a,0),( 0,b)]: a ,\ b in ...

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  3. Let S be the set of all rational numbers of the form m/n , where m i...

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  4. The binary operation**: RxxR->R is defined as a**b=2a+b. Find (2**3)**...

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  5. Let * be a binary operation of N given by a a*b=L C M (a , b) for all ...

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  6. Let * be a binary operation on Q-{0} defined by a*b=(a b)/2 for all...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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