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Let S={1,\ 2,\ 3,\ 4} and * be an operat...

Let `S={1,\ 2,\ 3,\ 4}` and `*` be an operation on `S` defined by `a*b=r ,` where `r` is the least non-negative remainder when product is divided by 5. Prove that `*` is a binary operation on `Sdot`

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- `\rightarrow` Binary operation.
- `\rightarrow` Closwre property.
I is closed under (0) operation
`a \cdot b \in S`
...
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RD SHARMA-BINARY OPERATIONS-Solved Examples And Exercises
  1. If the binary operation o. is defined on the set Q^+ of all positive r...

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

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

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

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

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

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

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

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  9. Let M be the set of all singular matrices of the form [xxxx] , wher...

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

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

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

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

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

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

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

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

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

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

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

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