Home
Class 12
MATHS
Let Z be the set of all integers and Z...

Let `Z` be the set of all integers and `Z_0` be the set of all non=zero integers. Let a relation `R` on `ZxxZ_0` be defined as follows: `(a , b)R(c , d) a d=b c` for all `(a , b),(c , d)ZxxZ_0` Prove that `R` is an equivalence relation on `ZxxZ_0dot`

Text Solution

Verified by Experts

Reflexivity:

`text { Let }(a, b) in Z times Z_{0}`

`Rightarrow a, b in Z, Z_{0}`

`Rightarrow a b=b 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

Let Z be the set of all integers and Z_0 be the set of all non=zero integers. Let a relation R on ZxZ_0 be defined as follows: (a , b)R(c , d) a d=b c for all (a , b),(c , d)ZxZ_0 Prove that R is an equivalence relation on ZxZ_0dot

Let Z be the set of all integers and Z_(0) be the set of all non-zero integers.Let a relation R on Z xx Z_(0) be defined as follows: (a,b)R(c,d)hArr ad=bc for all (a,b),(c,d)in Z xx Z_(0) Prove that R is an equivalence relation on Z xx Z_(0)

Let N be the set of all natural numbers and let R be a relation on N×N , defined by (a , b)R(c , d) iff a d=b c for all (a , b),(c , d) in N × Ndot . Show that R is an equivalence relation on N × N .

Let Z be the set of all integers and let a*b =a-b+ab . Then * is

Let Z be the set of all integers and let R be a relation on Z defined by a Rb implies a ge b . then R is

Let N be the set of all natural numbers and let R be a relation on N xx N, defined by (a,b)R(c,d)ad=bc for all (a,b),(c,d)in N xx N. Show that R is an equivalence relation on N xx N. Also,find the equivalence class [(2,6)].

Let A={1,2,3,~ 9}~ and~ R be the relation on A xx A defined by (a,b)R(c,d) if a+d=b+c for all (a,b),(c,d)in A xx A Prove that R is an equivalence relation and also obtain the equivalence class [(2,5)]

Let Z be the set of all integers, then , the operation * on Z defined by a*b=a+b-ab is

RD SHARMA-RELATIONS-Solved Examples And Exercises
  1. On the set N of all natural numbers, a relation R is defined as follow...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  11. Three relations R1, R2 and R3 are defined on set A={a , b , c} as foll...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |