Home
Class 12
MATHS
Let S be a relation on the set R of all ...

Let `S` be a relation on the set `R` of all real numbers defined by `S={(a ,\ b) in RxxR : a^2+b^2=1}` . Prove that `S` is not an equivalence relation on `R` .

Text Solution

Verified by Experts

We observe the following properties of `S`.

Reflexivity :

Let a be an arbitrary element of R. Then, `a \in R`

$$ \begin{aligned} ...
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

Let S be a relation on the set R of all real numbers defined by S={(a,b)epsilon RxR:a^(2)+b^(2)=1}. Prove that S is not an equivalence relation on R.

Let R be the relation on the set R of all real numbers defined by a Rb Iff |a-b|<=1 Then R is

Let R be a relation on the set of all real numbers defined by xRy hArr|x-y|<=(1)/(2) Then R is

The relation R, in the set of real number defined as R = {(a,b): a lt b} is:

S is a relation over the set R of all real numbers and it is given by (a,b)in S hArr ab>=0. Then S is :

Let R be a relation on the set Q of all rationals defined by R={(a,b):a,binQ" and "a-binZ}. Show that R is an equivalence relation.

Let S be the set of all rest numbers and lets R={(a,b):a,bin S and a=+-b}. Show that R is an equivalence relation on S.

Let R be a relation on the set of all lines in a plane defined by (l_(1),l_(2))in R line l_(1) is parallel to line l_(2). Show that R is an equivalence relation.

RD SHARMA-RELATIONS-Solved Examples And Exercises
  1. Let O be the origin. We define a relation between two points P and ...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  16. Define a reflexive relation.

    Text Solution

    |

  17. Define a symmetric relation.

    Text Solution

    |

  18. Define a transitive relation.

    Text Solution

    |

  19. Define an equivalence relation.

    Text Solution

    |

  20. If A={3,\ 5,\ 7} and B={2,\ 4,\ 9} and R is a relation given by is les...

    Text Solution

    |