Home
Class 12
MATHS
Let A be a set having more than one elem...

Let A be a set having more than one element. Let `'*'` be a binary operation on A defined by `a*b=sqrt(a^2 + b^2)` for all `a , b , in A`. Is `'*'` commutative or associative on A?

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 A be a set having more than one element. Let * be a binary operation on A defined by a*b=sqrt(a^2 + b^2) for all a , b , in Adot Is * commutative or associative on A?

Let A be a set having more than one element. Let * be a binary operation on A defined by a*b=sqrt(a^2 + b^2) for all a , b , in Adot Is * commutative or associative on A?

Let A be a set having more than one element. Let * be a binary operation on A defined by a*b=a for all a ,\ b in Adot Is * commutative or associative on A ?

Let A be any set containing more than one element. Let * be a binary operation on A defined by a*b=b for all a ,\ b in Adot Is * commutative A ?

Let * be a binary operation defined by a * b=3a+4b-2 . Find 4*5.

Let * be a binary operation on Z defined by a*b= a+b-4 for all a ,\ b in Zdot Show that * is both commutative and associative.

Let * be a binary operation on Q-{0} defined by a*b=(a b)/2 for all a ,\ b in Q-{0} . Prove that * is commutative on Q-{0} .

Let * be a binary operation on N defined by a*b=LCM(a ,\ b) for all a ,\ b in Ndot Find 2*4,\ 3*5,\ 1*6 .

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 '*' commutative on N ?

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

RD SHARMA ENGLISH-BINARY OPERATIONS-All Questions
  1. Define a binary operation * on the set A={0,1,2,3,4,5} given by a\**b...

    Text Solution

    |

  2. Let S={a+sqrt(2)b : a , b in Z}dot Then prove that an operation * on ...

    Text Solution

    |

  3. Let A be a set having more than one element. Let '*' be a binary ope...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |