Home
Class 12
MATHS
Let A={x in Z:0 le x le 12}. Show that R...

Let `A={x in Z:0 le x le 12}`. Show that `R={(a,b):a,b in A,|a-b|` is divisible by 4} is an equivalence relation. Find the set of all elements related to 1. Also write the equivalence class

Promotional Banner

Topper's Solved these Questions

  • SAMPLE PAPER 2019

    XII BOARDS PREVIOUS YEAR|Exercise Section D 35 B|1 Videos

Similar Questions

Explore conceptually related problems

Show that the relation R on the set A={x in Z:0<=x<=12}, given by R={(a,b):|a-b| is a multiple of 4} is an equivalence relation.Find the set of all elements related to 1 i.e.equivalence class [1]

Let R={(a,b):a,b in Z and (a-b) is divisible by 5}. Show that R is an equivalence relation on Z.

Show that the relation S in the set A={x in Z:0<=x<=12} given by S={(a,b):a,b epsilon Z,^(-)|a-b| is divisible by 4} is an equivalence relation.Find the set of all elements related to 1.

Show that each of the relation R in the set A={x in Z:0<=x<=12} given by (i) R={(a,b):|a-b| is a multiple of 4} (ii) quad R={(a,b):a=b} is an equivalence relation.Find the set of all elements related to 1 in each case.

Show that the relation R on the set A{x in Z;0<=12}, given by R={(a,b):a=b}, is an equivalence relation.Find the set of all elements related to 1.

Show that the relation R on the set A={x in Z;0<=x<=12}, given by R={(a,b):a=b}, is an equivalence relation.Find the set of all elements related to 1.

Prove that the relation R is the set A= {5,6,7,8,9,10} given by R= {(a, b) : |a - b| is divisible by 2} is an equivalence relation. Find the all elements related to the element 6.

Let R be the relation on set A={x:x in Z, 0 le x le 10} given by R={(a,b):(a-b) "is divisible by " 4} . Show that R is an equivalence relation. Also, write all elements related to 4.

Show that the relation R defined by R={(a,b):a-b is divisible by 3;a,b in Z} is an equivalence relation.

XII BOARDS PREVIOUS YEAR-XII Boards-All Questions
  1. Two numbers are selected at random(without replacement) from the first...

    Text Solution

    |

  2. Using elementary row transformations, find the inverse of the matrix A...

    Text Solution

    |

  3. Let A={x in Z:0 le x le 12}. Show that R={(a,b):a,b in A,|a-b| is divi...

    Text Solution

    |

  4. Show that the function f:R->R defined by f(x)=x/(x^2+1) AA x in R is n...

    Text Solution

    |

  5. If an operation ** on the set of integers Z is defined by a**b=2a^2+b ...

    Text Solution

    |

  6. Find the equation of the plane passing through the point <math> <mr...

    Text Solution

    |

  7. If A is a square matrix of order 2 and |A|=4, then find the value of |...

    Text Solution

    |

  8. Solve the following differential equation: x[dy]/[dx]sin(y/x)+x-ysin...

    Text Solution

    |

  9. Four cards are drawn one by one with replacement from a well-shuffled ...

    Text Solution

    |

  10. int1^5(|x-1|+|x-2|+|x-4|)\ dx

    Text Solution

    |

  11. Find the particular solution of the differential equation: (1+e^2x)dy+...

    Text Solution

    |

  12. The probability of two students A and B coming to school are 2/7 and 4...

    Text Solution

    |

  13. If y=(sinx)^x+sin^(-1)sqrt(1-x^2) then find (dy)/(dx)

    Text Solution

    |

  14. If x,y,z are different and Delta=|[x,x^2,x^3-1],[y,y^2,y^3-1],[z,z^2,z...

    Text Solution

    |

  15. Find the value of (x-y) from the matrix equation 2[(x,5),(7,y-3)]+[(-...

    Text Solution

    |

  16. int cos2x*cos4x*cos6x dx

    Text Solution

    |

  17. Solve the following differential equation: (y+3x^2)(dx)/(dy)=x

    Text Solution

    |

  18. Prove that sin^(-1)(4/5)+tan^(-1)(5/12)+cos^(-1)(63/65)=pi/2

    Text Solution

    |

  19. Find the angle between the line vec r = (2 hat i-hat j +3 hat k)+ lamb...

    Text Solution

    |

  20. Find the interval in which the function f given by f(x)=sin2x+cos2x, 0...

    Text Solution

    |