Home
Class 12
MATHS
Let S be the set of all real numbers exc...

Let S be the set of all real numbers except 1 and 'o' be an operation on S defined by : aob = a+b - ab for all a,b `in`S. Prove that the given operation is : (I) commutative (II) associative.

Promotional Banner

Topper's Solved these Questions

  • MODEL PAPER (1)

    PRADEEP PUBLICATION|Exercise EXERCISE|35 Videos

  • PROBABILITY

    PRADEEP PUBLICATION|Exercise EXERCISE|467 Videos

Similar Questions

Explore conceptually related problems

Let S be the set of all real numbers except 1 and 'o' be an operation on S defined by : aob = a+b - ab for all a,b in S. Prove that S is closed under given operation.

Let A be the set of all real numbers except - 1 and 'o' be the mapping form A xx A to A defined by a o b = a + b + ab for all a, b in A. Prove that the given operation is commutative.

Let A be the set of all real numbers except - 1 and 'o' be the mapping form A xx A to A defined by a o b = a + b + ab for all a, b in A. Prove that the given operation is associative.

Let a binary operation '*' be defined on Z by a * b = 2 a + 2b for all a, b in Z. Prove that the given operawtion is commutative but not associative.

Let a mapping '*' from R xx R to R be defined by a * b = 2 a + 2 b for all a , b in Z. Prove that the givne operation is commutative but not associative.

Let S be the set of all real numbers and let R be the relation in S defined by R = {(a,b), a leb^2 }, then

Let A be the set of all real numbers except - 1 and 'o' be the mapping form A xx A to A defined by a o b = a + b + ab for all a, b in A. Prove that 0(zero) is the identify element.

Let a binary operation '*' be defined on I (set of integers) by : a * b = 2a + 2b for a, b in I. Prove that given operation is commutative but not associative.

Let a mapping '*' from Q xx Q to Q (set of all rational numbers) be defined by a* b = a +2 b for all a, b in Q. Prove that the given operation is not commutative.

Let * be the binary operation defined on R by a * b = 1 + ab for all a, b in R, then the operation * is

PRADEEP PUBLICATION-MODEL PAPER (2)-EXERCISE
  1. Find the transpose of {:[(a,b),(c,d)]

    Text Solution

    |

  2. Evaluate: underset0overset(pi//2)int log(sinx)dx

    Text Solution

    |

  3. Let S be the set of all real numbers except 1 and 'o' be an operation ...

    Text Solution

    |

  4. Let A=Set of all real numbes except 1. Let * be defined as a+b-ab for...

    Text Solution

    |

  5. Let A=Set of all real numbes except 1. Let 'cdot' be defined as a+b-ab...

    Text Solution

    |

  6. Let A=Set of all real numbes except 1. Let 'cdot' be defined as a+b-ab...

    Text Solution

    |

  7. Prove that cot^-1 7 + cot^-1 8 + cot^-1 18 = cot^-1 3

    Text Solution

    |

  8. Solve the following equations sin(sin^(-1)""(1)/(5)+cos^(-1)x)=1

    Text Solution

    |

  9. Solve the following equations 5x-7y+z=11, 6x-8y-z=15, 3x+2y-6z=7 by Cr...

    Text Solution

    |

  10. Find dy/dx if x^y + y^x = a^b

    Text Solution

    |

  11. If f(x)={((x-5)/(|x-5|)+a" , if "xlt5),(a+b" , if "x=5),((x-...

    Text Solution

    |

  12. Find the interval of increase and decrease of the function f(x)=log(1+...

    Text Solution

    |

  13. Prove that the curves x=y^2 and xy=k cut at right angles* if 8k^2 =1

    Text Solution

    |

  14. int (sin^-1x)/(1-x^2)^(3//2) dx

    Text Solution

    |

  15. Evaluate: underset0 oversetpi int sinxdx .

    Text Solution

    |

  16. Sketch the graph of the function: y=f(x)={(x, if, 0lexle1),(1/x, if, 1...

    Text Solution

    |

  17. Solve the differential equation (d^2y)/(dx^2)=x+sinx given that when x...

    Text Solution

    |

  18. There is a group of 50 people who are patriotic out of which 20 believ...

    Text Solution

    |

  19. With the help of vector method, prove that,cosA=(b^2+c^2-a^2)/(2bc)

    Text Solution

    |

  20. Experiments show that radium decomposes at a rate proportioanl to the ...

    Text Solution

    |