Home
Class 12
MATHS
Is it true that every relation which ...

Is it true that every relation which is symmetric and transitive is also reflexive? Give reasons.

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

Give an example of a relation which is symmetric and transitive but not reflexive.

Give an example of a relation which is symmetric but neither reflexive nor transitive.

Let R be a relation defined by R={(a, b): a >= b, a, b in RR} . The relation R is (a) reflexive, symmetric and transitive (b) reflexive, transitive but not symmetric (c) symmetric, transitive but not reflexive (d) neither transitive nor reflexive but symmetric

Let R be the relation on the set A={1,\ 2,\ 3,\ 4} given by R={(1,\ 2),\ (2,\ 2),\ (1,\ 1),\ (4,\ 4),\ (1,\ 3),\ (3,\ 3),\ (3,\ 2)} . Then, R is reflexive and symmetric but not transitive (b) R is reflexive and transitive but not symmetric (c) R is symmetric and transitive but not reflexive (d) R is an equivalence relation

Let R be the relation on the set A={1,\ 2,\ 3,\ 4} given by R={(1,\ 2),\ (2,\ 2),\ (1,\ 1),\ (4,\ 4),\ (1,\ 3),\ (3,\ 3),\ (3,\ 2)} . Then, R is (a) reflexive and symmetric but not transitive (b) R is reflexive and transitive but not symmetric (c) R is symmetric and transitive but not reflexive (d) R is an equivalence relation

Give an example of a relation which is reflexive and symmetric but not transitive.

Give an example of a relation which is reflexive and transitive but not symmetric.

Given the relation R={(1,2),(2,3)} on the set A={1,2,3}, add a minimum number of ordered pairs so that the enlarged relation is symmetric, transitive and reflexive.

Given the relation R={(1,2),(2,3) on the set A={1,2,3}, add a minimum number of ordered pairs so that the enlarged relation is symmetric, transitive and reflexive.

Given the relation R={(1,\ 2),\ (2,\ 3)} on the set A={1,\ 2,\ 3} , add a minimum number of ordered pairs so that the enlarged relation is symmetric, transitive and reflexive.

RD SHARMA ENGLISH-RELATIONS-All Questions
  1. Let A={1,2,3}, and let R1="{"(1,1),(1,3),(3,1),(2,2")",(2,1),(3,3)}R2=...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  5. Show that the relation R defined by R={(a , b):a-b is divisible ...

    Text Solution

    |

  6. Test whether the following relations R1,R2"and"R3,"" are (i) reflex...

    Text Solution

    |

  7. Three relations R1, R2a n dR3 are defined on set A={a , b , c} as foll...

    Text Solution

    |

  8. Show that the relation R on the set A{xZ ;0lt=12}, given by R={(a ,...

    Text Solution

    |

  9. Let n be a fixed positive integer. Define a relation R on Z as f...

    Text Solution

    |

  10. Let Z be the set of all integers and Z0 be the set of all non zero...

    Text Solution

    |

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

    Text Solution

    |

  12. If R is an equivalence relation on a set A, then R^-1 is

    Text Solution

    |

  13. On the set N of all natural numbers, a relation R is defined as follow...

    Text Solution

    |

  14. If R1 and R2 are equivalence relations in a set A, show that R1nnR2...

    Text Solution

    |

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

    Text Solution

    |

  16. Let R be the equivalence relation in the set A={0,1,2,3,4,5} given b...

    Text Solution

    |

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

    Text Solution

    |

  18. Show that the relation geq on the set R of all real numbers is r...

    Text Solution

    |

  19. m is said to be related to n if m and n are integers and m-n is divisi...

    Text Solution

    |

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

    Text Solution

    |