Home
Class 12
MATHS
Discuss the commutativity and associativ...

Discuss the commutativity and associativity of the binary operation * on R defined by `a`*`b=(a b)/4for all a ,b in R.`

Text Solution

Verified by Experts

Let * be a binary operation on `R`
And it is defined by `a`*`b=(a b)/4`
Then we have to prove that * is associative on `R`
As , `a`*`b=(ab)/4`
Let a,b,c R
`(a`*`b)`*`c=((ba)/4)`*`c`
`(a`*`b)*c=(abc)/16`
...
Promotional Banner

Topper's Solved these Questions

  • ARITHMETIC PROGRESSION

    RD SHARMA|Exercise EXAMPLE|5 Videos

  • BINOMIAL DISTRIBUTION

    RD SHARMA|Exercise Solved Examples And Exercises|141 Videos

Similar Questions

Explore conceptually related problems

Discuss the commutativity and associativity of the binary operation * on R defined by a*b=(ab)/(4) for all a,b in R

Discuss the commutativity and associativity of the binary operation * on R defined by a*b=a-b+ab for all a,b in R, where on RHS we have usual addition,subtraction and multiplication of real numbers.

Discuss the commutativity and associativity of binary operation* defined on Q by the rule a*b=a-b+ab for all a,b in Q

Check the commutativity and associativity of * on R defined by a*b=a+b-7 for all a,b in Q.

Check the commutativity and associativity of * on Q defined by a*b=a-b for all a,b in Q

Check the commutativity and associativity of * on Z defined by a*b=a-b for all a,b in Z

Check the commutativity and associativity of * on Q defined by a*b=(ab)/(4) for all a,b in Q

Consider the binary operation on Z defined by a ^(*)b=a-b . Then * is

Check the commutativity and associativity of * on Q defined by a*b=a+ab for all a,b in Q.

Show that the binary operation * on Z defined by a*b=3a+7b is not commutative.

RD SHARMA-BINARY OPERATIONS-Solved Examples And Exercises
  1. Let A be a set having more than one element. Let * be a binary opera...

    Text Solution

    |

  2. Discuss the commutativity and associativity of the binary operation * ...

    Text Solution

    |

  3. Discuss the commutativity and associativity of the binary operation * ...

    Text Solution

    |

  4. Discuss the commutativity and associativity of binary operation * d...

    Text Solution

    |

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

    Text Solution

    |

  6. Let * be a binary operation on N given by a*b=H F C(a ,\ b) for all ...

    Text Solution

    |

  7. Let ** be the binary operation on N defined by a" "**" "b" "=" "Hd...

    Text Solution

    |

  8. Consider the binary operations*: RxxR->R and o: RxxR->R defined as a...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |