Home
Class 12
MATHS
If R and S are relations on a set A , th...

If `R` and `S` are relations on a set `A` , then prove the following: `R` and `S` are symmetric `=>RnnS` and `RuuS` are symmetric (ii) `R` is reflexive and `S` is any relation `=>RuuS` is reflexive.

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • PROBABILITY

    RD SHARMA ENGLISH|Exercise All Questions|449 Videos

  • SCALAR OR DOT PRODUCT

    RD SHARMA ENGLISH|Exercise All Questions|233 Videos

Similar Questions

Explore conceptually related problems

If R and S are relations on a set A , then prove the following : (i) R and S are symmetric RnnS and RuuS are symmetric, (ii) R is reflexive and S is any relation RuuS is reflexive.

If R and S are relations on a set A , then prove the following : R and S are symmetric RnnS and RuuS are symmetric R is reflexive and S is any relation RuuS is reflexive.

If R and S are transitive relations on a set A , then prove that RuuS may not be a transitive relation on A .

If R and S are transitive relations on a set A , then prove that RuuS may not be a transitive relation on Adot

If R and S are transitive relations on a set A , then prove that RuuS may not be a transitive relation on Adot

If R is a symmetric relation on a set A , then write a relation between R and R^(-1) .

Prove that a relation R on a set A is symmetric iff R=R^-1

Let R be a reflexive relation on a set A and I be the identity relation on A. Then

Prove that a relation R on a set A is symmetric iff R=R^(-1) .

Consider the relation perpendicular on a set of lines in a plane. Show that this relation is symmetric and neither reflexive and nor transitive

RD SHARMA ENGLISH-RELATIONS-All Questions
  1. Let S be a relation on the set R of all real numbers defined by S={(a ...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  12. If A={1,2,\ 3,\ 4} , B={1,4,9,16,25} and R be a relation defined from ...

    Text Solution

    |

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

    Text Solution

    |

  14. Define a reflexive relation.

    Text Solution

    |

  15. Define a symmetric relation.

    Text Solution

    |

  16. Define a transitive relation.

    Text Solution

    |

  17. Define an equivalence relation.

    Text Solution

    |

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

    Text Solution

    |

  19. A={1,\ 2,\ 3,\ 4,\ 5,\ 6,\ 7} and if R={(x ,\ y): y is one half of x ;...

    Text Solution

    |

  20. Let A={2,\ 3,\ 4,\ 5} and B={1,3,\ 4} . If R is the relation from A to...

    Text Solution

    |