Home
Class 12
MATHS
On Q, the set of all rational numbers, a...

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

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • APPLICATION OF INTEGRALS

    RD SHARMA ENGLISH|Exercise All Questions|163 Videos

  • BINOMIAL DISTRIBUTION

    RD SHARMA ENGLISH|Exercise All Questions|149 Videos

Similar Questions

Explore conceptually related problems

Let * be a binary operation on set Q-[1] defined by a*b=a+b-a b for all a , b in Q-[1]dot Find the identity element with respect to *onQdot Also, prove that every element of Q-[1] is invertible.

Let * be a binary operation on set Q-[1] defined by a*b=a+b-a b for all a , b in Q-[1]dot Find the identity element with respect to *onQdot Also, prove that every element of Q-[1] is invertible.

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 Qdot

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

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

Let * be a binary operation o Q defined by a*b= (ab)/4 for all a,b in Q ,find identity element in Q

On R-[1] , a binary operation * is defined by a*b=a+b-a b . Prove that * is commutative and associative. Find the identity element for * on R-[1]dot Also, prove that every element of R-[1] is invertible.

On the set Z of all integers a binary operation ** is defined by a**b=a+b+2 for all a ,\ b in Z . Write the inverse of 4.

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.

Let * be a binary operation on Q_0 (set of non-zero rational numbers) defined by a*b=(3a b)/5 for all a , b in Q_0dot Find the identity element.

RD SHARMA ENGLISH-BINARY OPERATIONS-All Questions
  1. If the binary operation * on the set Z is defined by a*b=a+b-5, then ...

    Text Solution

    |

  2. On the set Z of integers, if the binary operation * is defined by a*...

    Text Solution

    |

  3. On Q, the set of all rational numbers, a binary operation * is defined...

    Text Solution

    |

  4. Let * be a binary operation on set Q-[1] defined by a*b=a+b-a b for al...

    Text Solution

    |

  5. Show that the binary operation * on A=R-{-1} defined as a*b=a+b+a b fo...

    Text Solution

    |

  6. Let '*' be a binary operation on Q0 (set of all non-zero rational numb...

    Text Solution

    |

  7. Let '*' be a binary operation on Q0 (set of all non-zero rational numb...

    Text Solution

    |

  8. Let * be a binary operation on N given by a*b=LdotCdotM(a ,\ b) for ...

    Text Solution

    |

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

    Text Solution

    |

  10. Define a binary operation * on the set A={0,1,2,3,4,5} given by a*b=a ...

    Text Solution

    |

  11. On the set M=A(x)={[xxxx]: x in R}of2x2 matrices, find the identity ...

    Text Solution

    |

  12. Let X be a non-empty set and let * be a binary operation on P(X) (t...

    Text Solution

    |

  13. Let X be a nonempty set and *be a binary operation on P(X), the power ...

    Text Solution

    |

  14. Let X be a non-empty set and let * be a binary operation on P\ (X) ...

    Text Solution

    |

  15. Let X be a non-empty set and let * be a binary operation on P\ (X) ...

    Text Solution

    |

  16. Let A=QxxQ and let ** be a binary operation on A defined by (a ,\ b)...

    Text Solution

    |

  17. Let A=QxxQ and let * be a binary operation on A defined by (a ,\ b)...

    Text Solution

    |

  18. Let A=Nuu{0}xxNuu{0} and let * be a binary operation on A defined by...

    Text Solution

    |

  19. Let A=Nuu{0}xxNuu{0} and let * be a binary operation on A defined b...

    Text Solution

    |

  20. Let A=NxxN , and let * be a binary operation on A defined by (a ,\ ...

    Text Solution

    |