Home
Class 12
MATHS
Show that the relation R on the set A={x...

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

Text Solution

Verified by Experts

`a R a \Rightarrow a=a \forall a \in A`

hence `R` is reflexive

`a R b \Rightarrow a`=b`

...
Promotional Banner

Topper's Solved these Questions

  • PROBABILITY

    RD SHARMA|Exercise Solved Examples And Exercises|422 Videos

  • SCALAR OR DOT PRODUCT

    RD SHARMA|Exercise Solved Examples And Exercises|232 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]

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 in the set A={x: x in N,x <=10} given by R={(a, b):a+ b is even number] is an equivalence relation. Also find the set of all elements related to 3

Show that the relation R in the set A={x in N:0<=x<=12 } given by R={ (a,b):|a-b| is a multiple of 4 } is an equivalence relation?

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 the relation R in the set A = {1, 2, 3, 4, 5,6,7} given by R = {(a , b) : |a - b| " is even" } , is an equivalence relation.

Show that the relation R on the set A={1,2,3,4,5}, given by R={(a,b):|a-b| is even }, is an equivalence relation.Show that all the elements of {1,3,5} are related to each other and all the elements of {2,4} are related to each other.But,no element of {1,3,5} is related to any element of {2,4} .

Show that the relation R in the set A={1,2,3,4,5} given by R={(a,b):|a-b| is even }, is an equivalence relation.

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.

Show that the relation S on the set : A={x inZ:0lexle12} given by: S = { (a,b):a,binZ,|a-b| is divisible by 3} is an equivalence relation.

RD SHARMA-RELATIONS-Solved Examples And Exercises
  1. m is said to be related to n if m and n are integers and m-n is divisi...

    Text Solution

    |

  2. Let R be a relation on the set A of ordered pairs of integers defined ...

    Text Solution

    |

  3. Show that the relation R on the set A={x in Z ;0lt=xlt=12} , given by...

    Text Solution

    |

  4. Let L be the set of all lines in X Y -plane and R be the relation in L...

    Text Solution

    |

  5. Show that the relation R , defined on the set A of all polygons as R={...

    Text Solution

    |

  6. Let O be the origin. We define a relation between two points P and ...

    Text Solution

    |

  7. Let R be the relation defined on the set A={1,\ 2,\ 3,\ 4,\ 5,\ 6,\ 7}...

    Text Solution

    |

  8. Let S be a relation on the set R of all real numbers defined by S={(a ...

    Text Solution

    |

  9. Let Z be the set of all integers and Z0 be the set of all non-zero int...

    Text Solution

    |

  10. If R and S are relations on a set A , then prove the following: R and ...

    Text Solution

    |

  11. If R and S are transitive relations on a set A , then prove that RuuS ...

    Text Solution

    |

  12. Write the domain of the relation R defined on the set Z of integers as...

    Text Solution

    |

  13. If R={(x ,\ y): x^2+y^2lt=4; x ,\ y in Z} is a relation on Z , write ...

    Text Solution

    |

  14. Write the identity relation on set A={a ,\ b ,\ c} .

    Text Solution

    |

  15. Write the smallest reflexive relation on set A={1,\ 2,\ 3,\ 4} .

    Text Solution

    |

  16. If R={(x ,\ y): x+2y=8} is a relation on N , then write the range of R...

    Text Solution

    |

  17. If R is a symmetric relation on a set A , then write a relation betwee...

    Text Solution

    |

  18. Let R={(x ,\ y):|x^2-y^2|<1} be a relation on set A={1,\ 2,\ 3,\ 4,\ 5...

    Text Solution

    |

  19. If A={2,\ 3,\ 4} , B={1,\ 3,\ 7} and R={(x ,\ y): x in A ,\ y in B\ ...

    Text Solution

    |

  20. Let A={3,\ 5,\ 7} , B={2,\ 6,\ 10} and R be a relation from A to B def...

    Text Solution

    |