Home
Class 12
MATHS
Let A = N xx N and ** be the binary oper...

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.

Text Solution

Verified by Experts

`(a, b) ** (c, d) = (a+c, b, d)`
For commutative `(a, b) ** (c, d) = (c, d) ** (a, b)`
`(c, d) ** (a, b) = (c+a, d + b)`
Therefore A is commutative
`[(a, b) ** (c, d)] ** (e, f) = (a + c, b+d) ** (e, f) = (a + c + e, b+ d + f)`
`(a, b) ** [(c, d) ** (e, f)] = (a, b) ** (c + e, d +f) = (a + c + e, b + d + f)`
Hence A is associative
Promotional Banner

Topper's Solved these Questions

  • RELATIONS AND FUNCTIONS

    AAKASH INSTITUTE|Exercise Assignment (Section - A) Objective Type Questions (one option is correct)|102 Videos

  • RELATIONS AND FUNCTIONS

    AAKASH INSTITUTE|Exercise Assignment (Section - B) Objective Type Questions (one option is correct)|87 Videos

  • RELATIONS AND FUNCTIONS

    AAKASH INSTITUTE|Exercise Assignment (Section - J) Aakash Challengers Questions|8 Videos

  • PROBABILITY

    AAKASH INSTITUTE|Exercise ASSIGNMENT SECTION-J (aakash challengers questions)|13 Videos

  • SEQUENCES AND SERIES

    AAKASH INSTITUTE|Exercise Assignment (SECTION - J) Aakash Challengers|12 Videos

Similar Questions

Explore conceptually related problems

Let '**' be a binary operation defined on NxxN by : (a, b)**(c, d)=(a+c,b+d) . Prove that '**' is commutative and associative.

Let A=NN 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.

Let A=RR 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.

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

Let '**' be a binary operation on Q defined by : a**b=(2ab)/(3) . Show that '**' is commutative as well as 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 commutative on A.

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 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 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.

AAKASH INSTITUTE-RELATIONS AND FUNCTIONS -Try Yourself
  1. Find the domain and range of |x-3|.

    Text Solution

    |

  2. Find the domain and range of -|x-5|.

    Text Solution

    |

  3. Consider that [] represents greatest integer function. Find the valu...

    Text Solution

    |

  4. Consider that [] represents greatest integer function. [(3)/(5)] + [...

    Text Solution

    |

  5. Let f(x) = x^(3) + 5 and g(x) = 5x + 3 be two real functions. Find (f+...

    Text Solution

    |

  6. Let f(x) = 3x + 8 and g(x) = x^(2) be two real functions. Find (f+g) (...

    Text Solution

    |

  7. If f, g : R rarr R be defined respectively by f(x) = 3x + 2 and g(x) =...

    Text Solution

    |

  8. If f, g : R rarr R be defined respectively by f(x) = 8x + 7 and g(x) =...

    Text Solution

    |

  9. Let f(x) = x^(3) + 6x + 9 and g(x) = x+5 be two functions. Find (f+g) ...

    Text Solution

    |

  10. Let f(x) = x^(2) + 2x +5 and g(x) = x^(3) - 1 be two real functions. F...

    Text Solution

    |

  11. Show that the function f : R rarr R defined by f(x) = cos (5x+3) is ne...

    Text Solution

    |

  12. Let A be the set of all 50 students of class X I I in a central sch...

    Text Solution

    |

  13. If f: R->R be given by f(x)=s in^2x+s in^2(x+pi//3)+cosx\ cos(x+pi//3)...

    Text Solution

    |

  14. Let f : R rarr R and g : R rarr R be two functions such that fog (x) =...

    Text Solution

    |

  15. If f : [0, oo) rarr [2, oo) be defined by f(x) = x^(2) + 2, AA xx in R...

    Text Solution

    |

  16. Let f : N ->Rbe a function defined as f(x)=4x^2+12 x+15. Show that f ...

    Text Solution

    |

  17. If ** be a binary operation on N (the setof natural numbers) defined b...

    Text Solution

    |

  18. Let A = {1, 2, 3}. Find the number of binary operations on A.

    Text Solution

    |

  19. If a ** b = 4a^(2) + 6b^(2) be a binary operations on Q, then verify t...

    Text Solution

    |

  20. Let A = N xx N and ** be the binary opertation on A defined by (a, b) ...

    Text Solution

    |