Home
Class 12
MATHS
The following relations are defined on...

The following relations are defined on the set of real number: `a R bif1+a b >0` Find whether these relations are reflexive, symmetric or transitive.

Text Solution

Verified by Experts

Reflexivity:

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

a in R

Rightarrow 1+a times a>0

...
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

The following relations are defined on the set of real number: aRb if a-b>0 a Rb if 1+ab>0 aRb if |a|<=b Find whether these relations are reflexive, symmetric or transitive.

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

The following relations are defined on the set of real numbers. (i) a R b iff |a - b| gt 0 (ii) a R b iff |a| = |b| (iii) a R b iff |a| ge |b| (iv) a R b iff 1 + ab gt 0 (v) a R b iff |a| le b Find whether these relations are reflexive, symmetric or transitive.

aRb if a-b>0 is defined on the set of real numbers,find whether it is reflexive, symmetric or transitive.

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

aRb iff 1+ab>0 is defined on the set of real numbers,find whether it is reflexive, symmetric or transitive.

Show that the relation R in the set R of real numbers,defined as R={(a,b):a<=b^(2)} is neither reflexive nor symmetric nor transitive.

Show that the relations R on the set R of all real numbers,defined as R={(a,b):a<=b^(2)} is neither reflexive nor symmetric nor transitive.

Show that the relation R in the set of real numbers,defined as R={a,b):a<=b^(2)} is neither reflexive,nor symmetric,nor transitive.

RD SHARMA-RELATIONS-Solved Examples And Exercises
  1. Let a relation R1 on the set R of real numbers be defined as (a , b) ...

    Text Solution

    |

  2. Let S be the set of all points in a plane and R be a relation on S def...

    Text Solution

    |

  3. The following relations are defined on the set of real number: a ...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  6. Let N denote the set of all natural numbers and R be the relation on N...

    Text Solution

    |

  7. Let N be the set of all natural numbers and let R be a relation on N×N...

    Text Solution

    |

  8. Let R be a relation on the set of all line in a plane defined by (l1, ...

    Text Solution

    |

  9. Each of the following defines a relation on N: x -> y , (i) x , y in ...

    Text Solution

    |

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

    Text Solution

    |

  11. Given the relation R={(1,2),(2,3) on the set A={1,2,3}, add a minimum ...

    Text Solution

    |

  12. Let A={1,2,3,.....,9} and R be the relation in AxxA defined by (a ,b)R...

    Text Solution

    |

  13. Prove that the relation R on the set NxxN defined by (a ,\ b)R\ (c ,\ ...

    Text Solution

    |

  14. Let n be a positive integer. Prove that the relation R on the set Z o...

    Text Solution

    |

  15. Let "T" be the set of all triangles in a plane with "R" as relation ...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |