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Let A be a set having more than one elem...

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 Adot` Is `'*'` commutative or associative on A?

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Given
` a=b=frac{a bar{b}}{2}, forall a, b in Q` then
` forall a, b, sigma Q` we have
` a+(b+c)-a+(frac{b c}{2})-frac{a(frac{b c}{2})}{2}-frac{a b c}{4}`
` and (a+b)+c-frac{a b}{2}+c=frac{(frac{a bar{b}}{2}) c}{2}-frac{a b c}{4}`
therefore a` *(b * c)=(a * b)=c`
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RD SHARMA-BINARY OPERATIONS-Solved Examples And Exercises
  1. Define a binary operation * on the set A={0,1,2,3,4,5} given by a*b=a ...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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