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Let S={a+sqrt(2)b : a , b in Z}dot Then...

Let `S={a+sqrt(2)b : a , b in Z}dot` Then prove that an operation * on S defined by `(a_1+sqrt(2)b_1)*(a_2+sqrt(2)b_2)=(a_1+b_2)+sqrt(2)(b_1+b_2)` for all `b_1,a_2 in Z` is binary operation ofn `Sdot`

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Let S={a+sqrt(2)\ b\ : a ,\ b in Z}dot Then, prove that an operation * on S defined by (a_1+sqrt(2)b_1)*(a_2+sqrt(2)b_2)=(a_1+a_2)+sqrt(2)(b_1+b_2) for all a_1,\ a_2,\ b_1,\ b_2 in Z is a binary operation on Sdot

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Let A be a set having more than one element. Let '*' be a binary operation on A defined by a*b=sqrt(a^2 + b^2) for all a , b , in A . Is '*' commutative or associative on A?

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RD SHARMA ENGLISH-BINARY OPERATIONS-All Questions
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  2. Define a binary operation * on the set A={0,1,2,3,4,5} given by a\**b...

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  3. Let S={a+sqrt(2)b : a , b in Z}dot Then prove that an operation * on ...

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

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

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  6. Let S be the set of all rational numbers except 1 and * be defined on ...

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  7. Q, the set of all rational number, * is defined by a * b=(a-b)/2 , sho...

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  8. Find the identity element in set Q^+ of all positive rational numbers ...

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  9. If * defined on the set R of real numbers by a*b=(3a b)/7 , find the i...

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

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  11. If * is defined on the set R of all real numbers by a*b=sqrt(a^2+b^2) ...

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

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  13. Let * be a binary operation o Q defined by a*b= (ab)/4 for all a,bin Q...

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  14. If the binary operation o is defined on the set Q^+ of all positive ra...

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  15. Let S={a+sqrt(2)\ b\ : a ,\ b in Z}dot Then, prove that an operati...

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  16. Let S={1,\ 2,\ 3,\ 4} and * be an operation on S defined by a*b=r , wh...

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  17. Let S=(0,1,2,3,4,) and * be an operation on S defined by a*b=r , where...

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  18. Show that the operation vv and ^^ on R defined as avvb= Maximum of ...

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  19. On the set Q of all rational numbers an operation * is defined by a*b ...

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  20. On the set W of all non-negative integers * is defined by a*b=a^b ....

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