Home
Class 12
MATHS
Let A = N xx N and ∗ be the binary opera...

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.

Promotional Banner

Topper's Solved these Questions

  • RELATIONS AND FUNCTIONS

    PSEB|Exercise Exercise|118 Videos

  • PROBABILITY

    PSEB|Exercise Exercise|140 Videos

  • THREE DIMENSIONAL GEOMETRY

    PSEB|Exercise Exercise|77 Videos

Similar Questions

Explore conceptually related problems

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 = 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.

Let ** be binary operation on N defined by a ** b = HCF of a and b. Show that ** is both commutative and associative.

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 '*' 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 it exists.

Let A = N xx N being the set of natural numbers. Let '*' be a binary operation on A defined by (a,b) * (c,d) = (a+c,b+d). Show that '*' is commutative.

Let A = N xx N being the set of natural numbers. Let '*' be a binary operation on A defined by (a,b) * (c,d) = (a+c,b+d). Show that '*' is associative.

Let A = Q xx Q,Q being the set of rationals. Let '*' be a binary operation on A, defined by (a,b) * (c,d) = (ac,ad+b). Show that '*' is associative.

Let A= Q xx Q . Let'*' be a binary operation on A defined by: (a, b) * (c, d)= (ac, ad + b). Find the identity element of A

Let A = Q xx Q,Q being the set of rationals. Let '*' be a binary operation on A, defined by (a,b) * (c,d) = (ac,ad+b). Show that '*' is not commutative.

PSEB-RELATIONS AND FUNCTIONS-Exercise
  1. Let ∗ be a binary operation on the set Q of rational numbers as follow...

    Text Solution

    |

  2. Let ∗ be a binary operation on the set Q of rational numbers as follow...

    Text Solution

    |

  3. Let A = N xx N and ∗ be the binary operation on A defined by (a, b) *...

    Text Solution

    |

  4. State whether the following statement is true or false. Justify:For an...

    Text Solution

    |

  5. State whether the following statement is true or false. Justify: If ∗...

    Text Solution

    |

  6. Consider a binary operation ∗ on N defined as a * b = a^3 + b^3 Choose...

    Text Solution

    |

  7. Consider a binary operation ∗ on N defined as a * b = a^3 + b^3 Choose...

    Text Solution

    |

  8. Consider a binary operation ∗ on N defined as a * b = a^3 + b^3 Choose...

    Text Solution

    |

  9. Let f : RrarrR , be defined as f(x) = 10x + 7. Find the function g : ...

    Text Solution

    |

  10. Let f : WrarrW, be defined as f (n) = n – 1, if n is odd and f (n) = ...

    Text Solution

    |

  11. If f : R rarr R is defined by f(x) = x^2 – 3x + 2, find f (f (x)).

    Text Solution

    |

  12. Show that the function f : Rrarr {x in R : – 1 < x < 1} defined by f(x...

    Text Solution

    |

  13. Show that the function f : R rarr R given by f (x) = x^3 is injective...

    Text Solution

    |

  14. Give examples of two functions f : NrarrZ and g : ZrarrZ such that g ...

    Text Solution

    |

  15. Give examples of two functions f : NrarrN and g : NrarrN such that g o...

    Text Solution

    |

  16. Given a non empty set X, consider P(X) which is the set of all subsets...

    Text Solution

    |

  17. Find the number of all one-one functions from set A = {1, 2, 3} to its...

    Text Solution

    |

  18. Let S = {a, b, c} and T = {1, 2, 3}. Find F^–1 of the following funct...

    Text Solution

    |

  19. Let S = {a, b, c} and T = {1, 2, 3}. Find F^–1 of the following funct...

    Text Solution

    |

  20. Consider the binary operations * : RxxRrarrR and o : RxxRrarrR define...

    Text Solution

    |