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.

Text Solution

Verified by Experts

Let` A={a,b,c}`
Let `I_A` is an identity relation of `A.`
Then, `I_A ={(a,a),aϵA}
` So, identity relation will be reflexive.
Let R be reflexive relation such that
...
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

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

If a function is differentiable at a point,it is necessarily continuous at that point.But; the converse is not necessarily true.

Prove that every subset of a finite set is finite.

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.

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?

If the numbers of different reflexive relations on a set A is equal to the number of different symmetric relations on set A, then the number of elements in A is

Define a reflexive relation.

Let A={1, 2, 3) be a given set. Define a relation on A swhich is (i) reflexive and transitive but not symmetric on A (ii) reflexive and symmeetric but not transitive on A (iii) transitive and symmetric but not reflexive on A (iv) reflexive but neither symmetric nor transitive on A (v) symmetric but neither reflexive nor transitive on A (vi) transitive but neither reflexive nor symmetric on A (vii) neither reflexive nor symmetric and transitive on A (vii) an equivalence relation on A (ix) neither symmetric nor anti symmmetric on A (x) symmetric but not anti symmetric on A

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

RD SHARMA-RELATIONS-Solved Examples And Exercises
  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 "ge" on the set R of all real numbers is reflex...

    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

    |