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.

A

commutative

B

associative

C

Both (a) and (b)

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • RELATIONS AND FUNCTIONS-2

    DISHA PUBLICATION|Exercise EXERCISE-1: CONCEPT BUILDER (TOPICWISE) (TOPIC 3: Composite Function and Relation, Inverse of a Function, Binary Operations)|27 Videos

  • RELATIONS AND FUNCTIONS

    DISHA PUBLICATION|Exercise EXERCISE - 2|30 Videos

  • SEQUENCES AND SERIES

    DISHA PUBLICATION|Exercise Exercise -2 : Concept Applicator|30 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.

DISHA PUBLICATION-RELATIONS AND FUNCTIONS-2-EXERCISE-2: CONCEPT APPLICATOR
  1. If f(x)=x/(x-1), then (fofofo......of)(x) is equal to

    Text Solution

    |

  2. Statement-1: If f:R to R and g:R to R be two functions such that f(x)...

    Text Solution

    |

  3. Which of the following functions is NOT one-one ? 1. f:R to R defined...

    Text Solution

    |

  4. If f(x)=2x+abs(x),g(x)=1/3(2x-abs(x)) and h(x)=f(g(x)), domain of unde...

    Text Solution

    |

  5. If f(x)=sqrt(3|x|-x-2) and g(x)=sinx, then domain of (fog)(x) is

    Text Solution

    |

  6. Letf: A rarr B be a function then show that f is a bijection if and on...

    Text Solution

    |

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

    Text Solution

    |

  8. If the binary operation o. is defined on the set Q^+ of all positive r...

    Text Solution

    |

  9. Find the inverse of the function: f:(-oo,1]vec[1/2,oo],w h e r ef(x)=2...

    Text Solution

    |

  10. Let f:N rarr R be the function defined by f(x)=(2x-1)/2 and g:Q rarr Q...

    Text Solution

    |

  11. Let f(x)=(x+1)^2-1, xgeq-1. Then the set {x :f(x)=f^(-1)(x)} is {0,1,(...

    Text Solution

    |

  12. Let f(x)={(2x+a",",x ge -1),(bx^(2)+3",",x lt -1):} and g(x)={(x+4",...

    Text Solution

    |

  13. Let f :(4,6) uu (6,8) be a function defined by f(x) = x+[(x)/(2)] whe...

    Text Solution

    |

  14. Let [x] denot the greatest integer le x. If f (x)= [x] and g(x)=|x| th...

    Text Solution

    |

  15. Let f(x)=a x+ba n dg(x)=c x+d , a!=0. Assume a=1,b=2. If (fog)(x)=(gof...

    Text Solution

    |

  16. Let f(x)=x^(2)+3x-3, x ge0 if in points x(1),x(2),x(3),...x(n) are so ...

    Text Solution

    |

  17. "If "f:R to R, g:R and h:R to R be three functions are given by f(x)=x...

    Text Solution

    |

  18. Let g(x)=1+x-[x] and f(x)={{:(-1",", x lt 0),(0",",x=0),(1",", x gt 0)...

    Text Solution

    |

  19. Which of the following functions is the inverse of itself? f(x)=(1-x)/...

    Text Solution

    |

  20. Let f(x)=sinxa n dg(x)=(log)e|x|dot If the ranges of the composition f...

    Text Solution

    |