Home
Class 12
MATHS
Let ast be a binary operation on the set...

Let `ast` be a binary operation on the set of real numbers, defined by `a astb=frac[ab][5]`, for all `a,binR`. Show that `ast` is both commutative and associative.

Promotional Banner

Topper's Solved these Questions

  • MATRICES DETERMINANTS PROBABILITY

    USHA PUBLICATION|Exercise EXERCISE|59 Videos
  • PRACTICE PAPER

    USHA PUBLICATION|Exercise PRACTICE PAPER|95 Videos

Similar Questions

Explore conceptually related problems

Let ast be a binary operation on the set of real numbers, defined by a astb=frac[ab][5] , for all a,binR . Find the identity element.

Let ast be a binary operation on the set of real numbers, defined by a astb=frac[ab][5] , for all a,binR . Find the inverse elements.

Let *be a binary operation defined on R, the set of all real numbers, by a*b = sqrt(a^(2)+b^(2)), AA a, b in R. Show that is associative on R

Determine if the binaary operation o on the set R of real numbers defined by aob = a+b-3 AA a, b inR is commutative/ associative.

On the set R of real numbers, a binary operation o is defined by a0b=a+b+a^2b AA a, b inR . Prove that the operation is neither commutative nor associative.

Let A=N cup {0} xx N cup {0} and Let * be a binary operation on a defined by (a, b) **(c, d)=(a+c, b+d) for (a, b), (c, d) in N. Show that. (i) B commutative as A (ii) * is associative on A

Consider the binary operation **:R xxR to R and o:R xx R to R defined as a**b = |a-b| and a o b = a . For all a , b in R . Show that * is commutative but not associative, .o. is associative but not commutative.

If * is binary operation on set Q of rational numbers defined as a**b=(ab)/(5) . Write the identity for *, if any.

Let * is a binary operation on set of integers I defined by a**b=3a+4b-2 , then find the value of 4**5 .

USHA PUBLICATION-MODEL QUESTION SET-MODEL QUESTION SET
  1. Solve LPP : Maximize Z=20x1+30x2 subject to constraints 3x1+5x2le15, x...

    Text Solution

    |

  2. Solve sin^(-1)x +sin^(-1)(1-x) =(pi)/(2).

    Text Solution

    |

  3. Let ast be a binary operation on the set of real numbers, defined by a...

    Text Solution

    |

  4. Let ast be a binary operation on the set of real numbers, defined by a...

    Text Solution

    |

  5. Let ast be a binary operation on the set of real numbers, defined by a...

    Text Solution

    |

  6. If a relation R is defined on the set Z of integers as following (a,b)...

    Text Solution

    |

  7. If A=[[2,0,-3],[4,3,1],[-5,7,2]] is expressed as sum of a symmetric an...

    Text Solution

    |

  8. Given the equations x=cy+bz, y=az+cx and z=bx+ay where x,y and z a...

    Text Solution

    |

  9. Find A^2-5A+6 if A=[[2,0,1],[2,1,3],[1,-1,0]]

    Text Solution

    |

  10. Let a,b and c are real number and Delta=|{:(b+c,c+a,a+b),(c+a,a+b,b+...

    Text Solution

    |

  11. If A=[{:(cosalpha,-sinalpha),(sinalpha,cosalpha):}]andA+A'=I , then fi...

    Text Solution

    |

  12. Find the value of a and b if the function given below is continuous. ...

    Text Solution

    |

  13. If y=(sinx)^(tanx), find frac[dy][dx]

    Text Solution

    |

  14. If y=log[x+sqrt(x^(2)+1)], then prove that (x^(2)+1)(d^(2)y)/(dx^(2))+...

    Text Solution

    |

  15. Prove that all normals to the curve x = a cos t + at sin t, y = a sin ...

    Text Solution

    |

  16. If y=(tan^(-1)x)^2 then show that (x^2+1)^2 (d^2y)/(dx^2)+2x(x^2+1)((d...

    Text Solution

    |

  17. Find intsec^3xdx

    Text Solution

    |

  18. int0^(pi/2)sin2x log(tanx)dx

    Text Solution

    |

  19. Solve (1+x^2)frac[dy][dx]+2xy-4x^2=0 subject to the initial condition ...

    Text Solution

    |

  20. Evaluate: intfrac[x+3][sqrt(5-4x+x^2)]dx

    Text Solution

    |