Home
Class 12
MATHS
Test whether the following relations ...

Test whether the following relations `R_1,R_2"and"R_3,""` are (i) reflexive (ii) symmetric and (iii) transitive: `R_1` on `Q_0` defined by `(a , b)R_1 a=1/b` `R_2` on `Z` defined by `(a , b)R_2|a-b|lt=5` `R_3` on `R` defined by `(a , b)R_3 a^2-4a b+3b^2=0`

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

Test whether, R_1 on Q_0 defined by (a ,\ b) in R_1 a=1//b is (i) reflexive (ii) symmetric and (iii) transitive:

Test whether, R_2 on Z defined by (a ,\ b) in R_2 |a-b|lt=5 is (i) reflexive (ii) symmetric and (iii) transitive.

Test whether, R_3 on R defined by (a ,\ b) in R_3 a^2-4\ a b+3b^2=0 .

Check whether the relation R_1 in R defined by R_1 = {(a,b): a leb^3) is reflexive, symmetric ?

Check whether the relation R in R defined by R={(a ,b):alt=b^3} is reflexive, symmetric or transitive.

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

R={(b , c)} is defined on set A={a ,\ b ,\ c} . Find whether or not it is (i) reflexive (ii) symmetric (iii) transitive.

Determine whether each of the following relations are reflexive, symmetric and transitive : (i) Relation R in the set A= {1, 2, 3, …, 13, 14} defined as " " R = { (x, y ) : 3x - y =0}

R_(1) on Z defined by (a,b)inR_(1) " iff "|a-b|le7, R_(2) on Q defined by (a,b)inR_(2) " iff "ab=4 and R_(3) on R defined by (a, b)inR_(3)" iff "a^(2)-4ab+3ab^(2)=0 Relation R_(2) is

R_2={(a ,\ a)} is defined on set A={a ,\ b ,\ c} . Find whether or not it is (i) reflexive (ii) symmetric (iii) transitive.

RD SHARMA ENGLISH-RELATIONS-All Questions
  1. Let A={1,2,3} and R={(1,2),(1,1),(2,3)} be a relation on A . What ...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |