Home
Class 12
MATHS
Show that the number of binary operation...

Show that the number of binary operations on `{1," "2}` having 1 as identity and having 2 as the inverse of 2 is exactly one.

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

Determine the total number of binary operations on the set S={1,\ 2} having 1 as the identity element.

Let A = {1, 2, 3}. Find the number of binary operations on A.

Consider the binary operation * and o defined by the following tables on set S={a ,\ b ,\ c ,\ d} . (FIGURE) Show that both the binary operations are commutative and associative. Write down the identities and list the inverse of elements.

If A = {1, b}, then the number of binary operations that can be defined on A is

Q^+ denote the set of all positive rational numbers. If the binary operation o. on Q^+ is defined as a o.b=(a b)/2, then the inverse of 3 is

For the binary operation * on Z defined by a*b= a+b+1 the identity element is

Q^+ denote the set of all positive rational numbers. If the binary operation . on Q^+ is defined as a.b=(a b)/2, then the inverse of 3 is (a) 4/3 (b) 2 (c) 1/3 (d) 2/3

Show that a is the inverse of a for the addition operation + on R and 1/a is the inverse of a!=0 for the multiplication operation xx on R.

The number of commutative binary operations that can be defined on a set of 2 elements is

Show that -a is not the inverse of a in N for the addition operation + on N and 1/a is not the inverse of a in N for multiplication operation xx on N, for a!=1 .

RD SHARMA ENGLISH-BINARY OPERATIONS-All Questions
  1. Let A=NxxN , and let * be a binary operation on A defined by (a ,\ ...

    Text Solution

    |

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

    Text Solution

    |

  3. Show that the number of binary operations on {1," "2} having 1 as iden...

    Text Solution

    |

  4. Determine the total number of binary operations on the set S={1,\ 2...

    Text Solution

    |

  5. Let * be a binary operation on Z defined by a*b= a+b-4 for all a ,\ ...

    Text Solution

    |

  6. Let * be a binary operation on Z defined by a*b=a+b-4 for all a ,\ b...

    Text Solution

    |

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

    Text Solution

    |

  8. Let * be a binary operation on Q-{-1} defined by a*b=a+b+a b for all...

    Text Solution

    |

  9. Let * be a binary operation on Q-{-1} defined by a*b=a+b+a b for al...

    Text Solution

    |

  10. Let R0 denote the set of all non-zero real numbers and let A=R0xxR0...

    Text Solution

    |

  11. Let * be a binary operation on the set Q0 of all non-zero rational...

    Text Solution

    |

  12. On R-[1] , a binary operation * is defined by a*b=a+b-a b . Prove that...

    Text Solution

    |

  13. Let R0 denote the set of all non-zero real numbers and let A=R0xxR0 ...

    Text Solution

    |

  14. Let R0 denote the set of all non-zero real numbers and let A=R0xxR0 ...

    Text Solution

    |

  15. Let * be the binary operation on N defined by a*b=H C F of a and b ....

    Text Solution

    |

  16. Consider the set S={1,\ -1} of square roots of unity and multiplicatio...

    Text Solution

    |

  17. Consider the set S={1,\ omega,\ omega^2} of all cube roots of unity...

    Text Solution

    |

  18. Consider the set S={1,\ -1,\ i ,\ -i} of fourth roots of unity. Con...

    Text Solution

    |

  19. Consider the set S={1,\ 2,\ 3,\ 4} . Define a binary operation * on...

    Text Solution

    |

  20. Consider the infimum binary operation ^^ on the set S={1,\ 2,\ 3,\ ...

    Text Solution

    |