Home
Class 12
MATHS
Let S be the set of all rational numbers...

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

Text Solution

AI Generated Solution

To find the identity element for the operation defined on the set \( S \) of all rational numbers except 1, where the operation \( * \) is defined as: \[ a * b = a + b - ab \] we need to determine an element \( e \in S \) such that for any \( a \in S \): ...
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

Let S be the set of all rational number except 1 and * be defined on S by a*b=a+b-a b , for all a ,bSdot Prove that (i) * is a binary operation on ( i i ) * is commutative as well as associative.

Let A be the set of all real numbers except -1 and an operation 'o' be defined on A by aob = a+b + ab for all a, b in A , then identify elements w.r.t. 'o' is

Let Q be the set of all rational numbers and * be the binary operation , defined by a * b=a+ab for all a, b in Q. then ,

Let S be the set of all real numbers except -1 and let * be an operation defined by a*b=a+b+ab for all a,b in S. Determine whether * is a binary operation on S. If yes, check its commutativity and associativity.Also, solve the equation (2*x)*3=7

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.

Let '*' be a binary operation on Q_0 (set of all non-zero rational numbers) defined by a*b=(a b)/4 for all a , b in Q_0dot Then, find the identity element in Q_0 inverse of an element in Q_0dot

Let R be the set of real numbers and * be the binary operation defined on R as a*b= a+ b-ab AA a, b in R .Then, the identity element with respect to the binary operation * is

Let t be a binary operation on Q_(0)( set of non- zero rational numbers) defined by a*b=(3ab)/(5) for all a,b in Q_(0) Find the identity element.

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |