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

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 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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RD SHARMA ENGLISH-BINARY OPERATIONS-All Questions
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  2. If the binary operation o is defined on the set Q^+ of all positive ra...

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

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

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

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

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

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

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  9. On the set C of all complex numbers an operation 'o' is defined by ...

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  10. Let M be the set of all 2X2 real singular matrices . On M , let * be...

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  11. Determine whether * on N defined by a*b=a^b for all a ,\ b in N de...

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  12. Determine whether O on Z defined by a\ O\ b=a^b for all a ,\ b in ...

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  13. Determine whether * on N defined by a*b=a+b-2 for all a ,\ b in N ...

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  14. Determine whether 'xx6' on S={1,\ 2,\ 3,\ 4,\ 5} defined by axx6b= Rem...

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  15. Determine whether '+6' on S={0,\ 1,\ 2,\ 3,\ 4,\ 5} defined by a+6b={a...

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  16. 'o' on N defined by a o b= a b + b a for all a, b∈N define...

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  17. '*' on Q defined by a*b=(a-1)/(b+1) for all a ,\ b in Q define a bina...

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  18. Determine whether or not the definition of * On Z^+ , defined * by a...

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  19. Determine whether or not the definition of * On Z^+ , defined * by ...

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  20. Determine whether or not the definition of * On R , define by a*b=a...

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