Home
Class 12
MATHS
Q, the set of all rational number, * is ...

Q, the set of all rational number, * is defined by `a*b=(a-b)/2` , show that * is no associative.

Text Solution

Verified by Experts

Check associative :
Let` a, b, c in Q`
- is associative if,
`a+(b+c)=(a+b)+c `
` =a+(b+c)=a+(frac{b-c}{2}) `
...
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

On Q, the set of all rational numbers a binary operation * is defined by a*b=(a+b)/(2) Show that * is not associative on Q.

On the set Q of all rational numbers an operation * is defined by a*b=1+ab. show that * is a binary operation on Q.

On Q,the set of all rational numbers,a binary operation * is defined by a*b=(ab)/(5) for all a,b in Q. Find the identity element for * in Q Also,prove that every non-zero element of Q is invertible.

On the set Q of all rational numbers if a binary operation * is defined by a*b=(ab)/(5), prove that * is associative on Q.

If the operation * is defined on the set Q of all rational numbers by the rule a*b=(ab)/(3) for all a,b in Q. Show that * is associative on Q

Let *, be a binary operation on N, the set of natural numbers defined by a*b = a^b, for all a,b in N. is * associative or commutative on N?

On Z, the set of all integers,a binary operation * is defined by a*b=a+3b-4 Prove that * is neither commutative nor associative on Z.

Let * be a binary operation on N, the set of natural numbers, defined by a*b= a^b for all a , b in Ndot Is '*' associative or commutative on N ?

Let 'o' be a binary operation on the set Q_0 of all non-zero rational numbers defined by a\ o\ b=(a b)/2 , for all a ,\ b in Q_0 . Show that 'o' is both commutative and associate (ii) Find the identity element in Q_0 (iii) Find the invertible elements of Q_0 .

Let S be the set of all rational numbers except 1 and * be defined on S by a*b=a+b-ab, for alla ,b in S. Find its identity element

RD SHARMA-BINARY OPERATIONS-Solved Examples And Exercises
  1. Let A=NxNa n d^(prime)*' be a binaryoperation on A defined by (a , b)*...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |