Home
Class 12
MATHS
Let A = Q - (0), where Q is the set of r...

Let A = Q - (0), where Q is the set of rationals. Let * : `A xx A rarr A` be defined as `a*b = (3ab)/(5)` for all a,b `in` A. Check whetehr * is commutative or associative. Find the identity element for * and inverse of a in` A (if it exists).

Promotional Banner

Topper's Solved these Questions

  • RELATIONS AND FUNCTIONS

    PRADEEP PUBLICATION|Exercise EXERCISE|401 Videos

  • PROBABILITY

    PRADEEP PUBLICATION|Exercise EXERCISE|467 Videos

  • THREE DIMENSIONAL GEOMETRY

    PRADEEP PUBLICATION|Exercise EXERCISE|373 Videos

Similar Questions

Explore conceptually related problems

Let * : Q xx Q rarr Q be defined a as a * b = 1 + ab for all a, b in Q. Show that * is commutative but not associative.

Let A = N xx N , N being the set of natural numbers. Let * : A xx A rarr A be defined as (a,b)*(c,d) = (ad+bc,bd) for all (a,b), (c,d) in A. Show that '*' is commutative

Let A = N xx N , N being the set of natural numbers. Let * : A xx A rarr A be defined as (a,b)*(c,d) = (ad+bc,bd) for all (a,b), (c,d) in A. Show that '*' is associative.

In the binary operation *: Q xx Q rarr Q is defined as : a*b = a + b - ab, a,b in Q Show that * is commutative .

In the binary operation *: Q xx Q rarr Q is defined as : a**b = a +b + ab, a,b in Q Show that * is commutative.

let A = N xxN and * be the binary operation on A defined by : (a,b) * (c,d) = (a+c,b+d) . Show that * is commutative and associative. Find the identify element for * on A, if any.

Let A = N xx N and ∗ be the binary operation on A defined by (a, b) * (c, d) = (a + c, b + d) Show that ∗ is commutative and associative. Find the identity element for ∗ on A, if any.

In the binary operation *: Q xx Q rarr Q is defined as : a**b=(ab)/4, a,b inQ Show that * is commutative.

Let '*' be a binary operation on Q defined by : a* b = (3ab)/5 . Show that * is commutative as well as associative. Also find its identity element, if its exists.

Let A = R xx R and * be a binary operation on A defined by : (a,b) * (c,d) = (A+c,b+d) . Show that * is commutative and associative. Find the identity element for * on A. Also find the inverse of every element (a,b) in A.

PRADEEP PUBLICATION-RELATIONS AND FUNCTIONS-EXERCISE
  1. Let A = Q - (0), where Q is the set of rationals. Let * : A xx A rarr ...

    Text Solution

    |

  2. Let A = (a,b,c) and R be the relation defined on A as follows R = (a,a...

    Text Solution

    |

  3. Let A = (6,7,8,10), B = (2,4,5) a inA , b in B and R be the relation f...

    Text Solution

    |

  4. For the given relation R on a set S, determine which are equivalence r...

    Text Solution

    |

  5. For the given relation R on a set S, determine which are equivalence r...

    Text Solution

    |

  6. For the given relation R on a set S, determine which are equivalence r...

    Text Solution

    |

  7. In the following cases, for the given relation R on the set S, determi...

    Text Solution

    |

  8. In the following cases, for the given relation R on the set S, determi...

    Text Solution

    |

  9. For the given relation R on a set S, determine which are equivalence r...

    Text Solution

    |

  10. Check whether the relation R defined in the set (1, 2, 3, 4, 5, 6) as ...

    Text Solution

    |

  11. Show that R= {(a, b): a ge b} is reflexive and transitive but not sym...

    Text Solution

    |

  12. Let A be the set of human beings living in a town at a particular time...

    Text Solution

    |

  13. Given the relation R = {(1, 2), (2, 3)} on the set of natural numbers,...

    Text Solution

    |

  14. Show that each of the relation R in the set A ={x in z : 0 le x le 12}...

    Text Solution

    |

  15. Show that each of the relation R in the set A = {x in Z : 0 le x le 12...

    Text Solution

    |

  16. Is inclusion of a subset in another, in the context of a universal set...

    Text Solution

    |

  17. If R is a relation in N xx N, show that the relation R defined by (a, ...

    Text Solution

    |

  18. If R is the relation in N xx N defined by (a, b) R (c,d) if and only i...

    Text Solution

    |

  19. Show that the relation R defined by (a, b) R(c,d)implies a+d=b+c in...

    Text Solution

    |

  20. Each of the following defines a relation R in N. x R y if xy is squa...

    Text Solution

    |

  21. Each of the following defines a relation R in N. x R y if xy is squa...

    Text Solution

    |