Home
Class 12
MATHS
Let * be a binary operation on Q-{0} ...

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}` .

Text Solution

Verified by Experts

Let * be a binary operation on `Q-{0}`
And it is defined by `a`*`b=(a b)/2`
Then we have to prove that * is commutative on `Q-{0}`
`a`*`b=(ab)/2`
`a`*`b=(ba)/2`
`a`*`b=b`*`a`
Hence Proved.
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 * be a binary operation on Q-{-1} defined by a*b=a+b+ab for all a,b in Q-{-1}. Then,Show that * is both commutative and associative on Q-{-1} (ii) Find the identity element in Q-{-1}

Let A=N uu{0}xx N uu{0} and let * be a binary operation on A defined by (a,b)*(c,d)=(a+c,b+d) for all (a,b),(c,d)in A. Show that * is commutative on A.

Let * be a binary operation on N defined by a*b = a^(b) for all a,b in N show that * is neither commutative nor associative

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

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

Let A=N uu{0}xx N uu{0} and let * be a binary operation on A defined by (a,b)*(c,d)=(a+c,b+d) for all (a,b),(c,d)in A* show that * is associative on A.

Let ^(*) be a binary operation on Q-{-1} defined by a*b=a+b+ab for all a,b in Q-{-1}. Then,Show that every element of Q-{-1} is invertible.Also,find the inverse of an arbitrary element.

Show that the operation '**' on Q - {1} defined by a**b=a+b-ab for all a,binQ-{1} , satisfies the commutative law.

Let A=NxxN , and let * be a binary operation on A defined by (a , b)*(c , d)=(a d+b c , b d) for all (a , b), (c , d) in NxxNdot Show that: * is commutative on Adot (ii) * is associative on Adot

RD SHARMA-BINARY OPERATIONS-Solved Examples And Exercises
  1. The binary operation**: RxxR->R is defined as a**b=2a+b. Find (2**3)**...

    Text Solution

    |

  2. Let * be a binary operation of N given by a a*b=L C M (a , b) for all ...

    Text Solution

    |

  3. Let * be a binary operation on Q-{0} defined by a*b=(a b)/2 for all...

    Text Solution

    |

  4. Let A be a set having more than one element. Let * be a binary opera...

    Text Solution

    |

  5. If the operation * is defined on the set Q of all rational numbers ...

    Text Solution

    |

  6. Examine whether the binary operation ** defined on R by a**b=a b+1 i...

    Text Solution

    |

  7. Let A be a set having more than one element. Let * be a binary opera...

    Text Solution

    |

  8. Discuss the commutativity and associativity of the binary operation * ...

    Text Solution

    |

  9. Discuss the commutativity and associativity of the binary operation * ...

    Text Solution

    |

  10. Discuss the commutativity and associativity of binary operation * d...

    Text Solution

    |

  11. Let * be a binary operation on N, the set of natural numbers, defined ...

    Text Solution

    |

  12. Let * be a binary operation on N given by a*b=H F C(a ,\ b) for all ...

    Text Solution

    |

  13. Let ** be the binary operation on N defined by a" "**" "b" "=" "Hd...

    Text Solution

    |

  14. Consider the binary operations*: RxxR->R and o: RxxR->R defined as a...

    Text Solution

    |

  15. Let A be a non-empty set and S be the set of all functions from A t...

    Text Solution

    |

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

    Text Solution

    |

  17. Let A be a set having more than one element. Let * be a binary oper...

    Text Solution

    |

  18. Let * be a binary operation on N defined by a*b=1. cdotmdot(a ,\ b)...

    Text Solution

    |

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

    Text Solution

    |

  20. Determine whether * on N defined by a*b=1 for all a ,\ b in N is asso...

    Text Solution

    |