Home
Class 12
MATHS
Let * be a binary operation on Z defi...

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.

Text Solution

Verified by Experts

Commutative
a * b = a + b – 4
`= b + a – 4`
`= b * a`
`forall a, b, in Z`

Associative
`a * (b * c) = a * (b + c – 4)` ...
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 * 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 R_(0) denote the set of all non-zero real numbers and let A=R_(0)xx R_(0) .If * is a binary operation on A defined by (a,b)*(c,d)=(ac,bd) for all (a,b),(c,d)in A* show that * is both commutative and associative on A( ii) Find the identity element in A

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

Let A=NxNa n d^(prime)*' be a binaryoperation on A defined by (a , b)*(C , d)=(a c , b d) for all a , b , c , d , in Ndot Show that '*' is commutative and associative binary operation on A.

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

Let A = N xx N and ** be the binary opertation on A defined by (a, b) ** (c, d) = (a+c, b+d) . Show that ** is commutative and associative.

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

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.

RD SHARMA-BINARY OPERATIONS-Solved Examples And Exercises
  1. Show that the number of binary operations on {1," "2} having 1 as iden...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  9. Let 'o' be a binary operation on the set Q0 of all non-zero rati...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  18. \begin{tabular}{|l|l|l|l|l|l|} \hline 1 & 1 & 2 & 3 & 4 & 5 \\ \hline ...

    Text Solution

    |

  19. Consider a binary operation * on the set {1, 2, 3, 4, 5} given by t...

    Text Solution

    |

  20. Define a binary operation * on the set A={0,\ 1,\ 2,\ 3,\ 4,\ 5} as...

    Text Solution

    |