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Let A=NxNa n d^(prime)*' be a binaryoper...

Let `A=NxNa n d^(prime)*'` be a binaryoperation on A defined by `(a , b)*(C , d)=(a c , b d)` for all `a , b , c , d , in Ndot` Show that `'*'` is commutative and associative binary operation on A.

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To check associative
Let `(a,b),(c,d),(e,f) in A`
Now, `(a,b){(c,d).(e,f)}=(a,b)(ce,df)`
`=a(ce),b(df)`
`=((ac)e,(bd)f)`
`=(ac,bd).(ef)`
`={(a,b).(c,d)}.(e,f)`
`(a,b){(c,d).(e,f)}={(a,b).(c,d)}.(e,f)`
...
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RD SHARMA-BINARY OPERATIONS-Solved Examples And Exercises
  1. Consider the binary operations*: RxxR->R and o: RxxR->R defined as a...

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

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

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

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  5. Let * be a binary operation on N defined by a*b=1. cdotmdot(a ,\ b)...

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  6. Let '*' be a binary operation on N given by a*b=LdotCdotMdot(a , b) fo...

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  7. Determine whether * on N defined by a*b=1 for all a ,\ b in N is asso...

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  8. Determine whether * on Q defined by a*b=(a+b)/2 for all a ,\ b in Q i...

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  9. Let A be any set containing more than one element. Let * be a binar...

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  10. Check the commutativity and associativity of * on Z defined by a*b=...

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  11. Check the commutativity and associativity of * on N defined by a*b=...

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  12. Check the commutativity and associativity of * on Q defined by a*b=...

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  13. Check the commutativity and associativity of O on Q defined by a\ \...

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  14. Check the commutativity and associativity of o on Q defined by a\ o...

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  15. Check the commutativity and associativity of * on Q defined by a*b=...

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  16. Check the commutativity and associativity of * on Q defined by a*b=...

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  17. Check the commutativity and associativity of * on R defined by a*b=...

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  18. Check the commutativity and associativity of * on Q defined by a*b=...

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  19. Check the commutativity and associativity of * on Q defined by a*b=...

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

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