Home
Class 12
MATHS
Check the following relations R and S fo...

Check the following relations `R` and `S` for reflexivity, symmetry and transitivity: (i)`a R b` iff `b` is divisible by `a ,\ a ,\ b in N` (ii) `l_1` `S\ l_2` iff `l_1_|_l_2` , where `l_1` and `l_2` are straight lines in a plane.

Text Solution

Verified by Experts

The relation R is reflexive, since a is divisible by a
R is not symmetric because b is divisible by a but a is not divisible by b. i.e., `aRb ⇒ bRa`
Again, R is transitive, since b is divisible by a and c
is divisible by b, then always c is divisible by a
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

Straight Lines L1

Straight Line L1

In the following circuit find l_1 and l_2 :-

Let R be the relation over the set of all straight lines in a plane such that l_(1) R l_(2) iff l_(1) _|_ l_(2) . Then, R is

If l is the set of integers and if the relation R is defined over l by aRb, iff a - b is an even integer, a,b inl , the relation R is

Let R be the relation over the set of all straight lines in a plane such that l_1\ R\ l_2hArrl_1_|_l_2 . Then, R is (a) symmetric (b) reflexive (c) transitive (d) an equivalence relation

Equation of a line segment in first quadrant is given as 4x+5y=20 , two lines l_1 , and l_2 are trisecting given line segment. If l_1 and l_2 pass through the origin the find then tangent of angle between l_1 , and l_2 .

Let A be a relation on the set of all lines in a plane defined by (l_(2), l_(2)) in R such that l_(1)||l_(2) , the n R is

Let R be a relation on the set of all lines in a plane defined by (l_(1),l_(2))in R line l_(1) is parallel to line l_(2). Show that R is an equivalence relation.

Let R be a relation on the set of all line in a plane defined by (l_(1),l_(2))in R hArr l in el_(1) is parallel to line l_(2). Show that R is an equivalence relation.

RD SHARMA-RELATIONS-Solved Examples And Exercises
  1. Show that the relation R on the set A={1,\ 2,\ 3} given by R={(1,\ 1),...

    Text Solution

    |

  2. Show that the relation R on the set A={1,\ 2,\ 3} given by R={(1,\ 2),...

    Text Solution

    |

  3. Check the following relations R and S for reflexivity, symmetry and tr...

    Text Solution

    |

  4. Let a relation R1 on the set R of real numbers be defined as (a ,\ b) ...

    Text Solution

    |

  5. Determine whether Relation R on the set A={1,\ 2,\ 3,\ ,\ 13 ,\ 14} d...

    Text Solution

    |

  6. Determine whether Relation R on the set N of all natural numbers def...

    Text Solution

    |

  7. Determine whether Relation R on the set A={1,\ 2,\ 3,\ 4,\ 5,\ 6} defi...

    Text Solution

    |

  8. Determine whether Relation R on the set Z of all integer defined as R=...

    Text Solution

    |

  9. Show that the relation R on R defined as R={(a ,\ b): alt=b} , is refl...

    Text Solution

    |

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

    Text Solution

    |

  11. Let X={1,\ 2,\ 3,\ 4,\ 5,\ 6,\ 7,\ 8,\ 9} , Let R1 be a relation on X ...

    Text Solution

    |

  12. Show that the relations R on the set R of all real numbers, defined as...

    Text Solution

    |

  13. Let A={1,\ 2,\ 3} . Then, show that the number of relations contain...

    Text Solution

    |

  14. Let A be the set of all human beings in a town at a particular time...

    Text Solution

    |

  15. Let A be the set of all human beings in a town at a particular time...

    Text Solution

    |

  16. Let A be the set of all human beings in a town at a particular time...

    Text Solution

    |

  17. Let A be the set of all human beings in a town at a particular time...

    Text Solution

    |

  18. R1={(a ,\ a),\ (a ,\ b),\ (a ,\ c),\ (b ,\ b),\ (b ,\ c),\ (c ,\ a),\ ...

    Text Solution

    |

  19. R2={(a ,\ a)} is defined on set A={a ,\ b ,\ c} . Find whether or not ...

    Text Solution

    |

  20. R3={(b , c)} is defined on set A={a ,\ b ,\ c} . Find whether or not i...

    Text Solution

    |