Home
Class 12
MATHS
Prove that every identity relation on a ...

Prove that every identity relation on a set is reflexive, but the converse is not necessarily true.

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

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

If A={a,b,c,d}, then on A . (i) write the identity relation I_(A) . (ii) write a reflexive relation which is not the identity relation.

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

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

Prove that the identity function on real numbers given by f(x) = x is continuous at every real number.

If P+Q=0 . Then which of the following is necessarily true?

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

Assertion and Reason type questions :Consider the following statements, p: Every reflexive relation is a symmetric relation, q: Every anti-symmetric relation is reflexive.Which of the following is/ are true?

Assertion and Reason type questions :Consider the following statements, p: Every reflexive relation is a symmetric relation, q: Every anti-symmetric relation is reflexive.Which of the following is/ are true?

The smallest reflexive relation on the set A {1, 2, 3} is

RD SHARMA ENGLISH-RELATIONS-All Questions
  1. Check whether the relation R defined on the set A={1,\ 2,\ 3,\ 4,\ 5,\...

    Text Solution

    |

  2. Check whether the relation R on R defined by R={(a ,\ b): alt=b^3} is ...

    Text Solution

    |

  3. Prove that every identity relation on a set is reflexive, but the c...

    Text Solution

    |

  4. If A={1,\ 2,\ 3,\ 4} define relations on A which have properties of be...

    Text Solution

    |

  5. If A={1,\ 2,\ 3,\ 4} define relations on A which have properties of be...

    Text Solution

    |

  6. If A={1,\ 2,\ 3,\ 4} define relations on A which have properties of be...

    Text Solution

    |

  7. Let R be a relation defined on the set of natural numbers N as R={(...

    Text Solution

    |

  8. Is it true that every relation which is symmetric and transitive is...

    Text Solution

    |

  9. An integer m is said to be related to another integer n if m is a mult...

    Text Solution

    |

  10. Show that the relation "geq" on the set R of all real numbers is refle...

    Text Solution

    |

  11. Give an example of a relation which is reflexive and symmetric but ...

    Text Solution

    |

  12. Give an example of a relation which is reflexive and transitive but...

    Text Solution

    |

  13. Give an example of a relation which is symmetric and transitive but...

    Text Solution

    |

  14. Give an example of a relation which is symmetric but neither reflex...

    Text Solution

    |

  15. Give an example of a relation which is transitive but neither refle...

    Text Solution

    |

  16. Given the relation R={(1,\ 2),\ (2,\ 3)} on the set A={1,\ 2,\ 3} , ad...

    Text Solution

    |

  17. Let A={1,\ 2,\ 3} and R={(1,\ 2),\ (1,\ 1),\ (2,\ 3)} be a relation on...

    Text Solution

    |

  18. Let A={a , b , c) and the relation R be defined on A as follows: R={(a...

    Text Solution

    |

  19. Each of the following defines a relation on N : (i) x+y=...

    Text Solution

    |

  20. Let R be a relation on the set of all lines in a plane defined by (l...

    Text Solution

    |