Home
Class 12
MATHS
Show that the relation R in the set of a...

Show that the relation R in the set of all natural number, N defined by is an `R = {(a , b) : |a - b| "is even"}` in an equivalence relation.

Text Solution

Verified by Experts

The correct Answer is:
R is an equivalence relation
Promotional Banner

Topper's Solved these Questions

  • RELATIONS AND FUNCTIONS

    SUBHASH PUBLICATION|Exercise SIX MARKS QUESTIONS WITH ANSWERS|7 Videos

  • RELATIONS AND FUNCTIONS

    SUBHASH PUBLICATION|Exercise TRY YOURSELF - EXERCISE (One mark questions)|5 Videos

  • RELATIONS AND FUNCTIONS

    SUBHASH PUBLICATION|Exercise TWO MARKS QUESTIONS WITH ANSWERS|15 Videos

  • PUC SUPPLEMENTARY EXAMINATION QUESTION PAPER JUNE 2019

    SUBHASH PUBLICATION|Exercise PART E|4 Videos

  • SUPER MODEL QUESTION PAPER FOR PRACTICE

    SUBHASH PUBLICATION|Exercise PART - E|4 Videos

Similar Questions

Explore conceptually related problems

Define an equivalence relation.

Show that the relation R in the set of all integers, Z defined by R = {(a, b) : 2 "divides" a - b} is an equivalence relation.

Show that the relation R in the set A = {x in Z : 0 le x le 12} given by R = {a , b) : |a - b| is a multiple of 4} is an equivalence relation.

Show thaT the relation R in the set of all integers Z defined by R{(a,b) : 2 divides a-b} is an equivalence relation.

Let R be the relation on the set R of all real numbers defined by a R b Iff |a-b| le1. Then R is

Prove that the relation R in the set of integers z defined by R = { ( x , y) : x-y is an integer } is an equivalence relation.

Show that the relation R in the set A = {1,2,3,4,5} given by R = {(a,b) : |a-b| is even}, is an equivalence relation. Show that all the elements of {1,3,5} are related to each other and all the elements of {2,4} are related to each other. But no element of {1,3,5} is related to any element of {2,4}.

Prove that the relation R in the set of integers Z defined by R = {(x,y) : x - y. is an integer) is an equivalence relation.

Show that the relation R in R (Set of real numbers) is defined as R = {(a,b) : aleb} is reflexive and transitive but not symmetric.

SUBHASH PUBLICATION-RELATIONS AND FUNCTIONS -THREE MARKS QUESTIONS WITH ANSWERS
  1. Verify whether the function f : A to B , where A = R - {3} and B = R -...

    Text Solution

    |

  2. If * is a binary operation defined on A = N xx N by (a , b) ** (c, d) ...

    Text Solution

    |

  3. Show that the relation R in the set of all integers, Z defined by R = ...

    Text Solution

    |

  4. Show that the relation R in the set of all natural number, N defined b...

    Text Solution

    |

  5. Show that the relation R in the set A = {x in Z : 0 le x le 12} given ...

    Text Solution

    |

  6. Let R be relation on the set A = {1,2,3,.....,14} by R = {(x,y):3x - y...

    Text Solution

    |

  7. Relation R on Z defined as R = {(x ,y): x - y "is an integer"}. Show t...

    Text Solution

    |

  8. Show that the relation R in R defined R = {(a, b) : a le b} is reflexi...

    Text Solution

    |

  9. Show that if f : R - {7/5} to R - {3/5} is defined by f(x) = (3x + 4)/...

    Text Solution

    |

  10. Show that if f : A to B and g: B to C are one-one, then gof: A to C is...

    Text Solution

    |

  11. Show that if f: A to B and g: B to C are onto, then gof : A to C is al...

    Text Solution

    |

  12. Consider f: N to N, g : N to N and h: N to R defined as f(x) = 2x, g(y...

    Text Solution

    |

  13. If f: X to Y, g : Y to Z and h: Z to S are functions, then ho(gof) = (...

    Text Solution

    |

  14. Let f: X to Y and g: Y to Z be two invertible functions. Then gof is ...

    Text Solution

    |

  15. If R(1) and R(2) are equivalence relations in a set A, show that R(1) ...

    Text Solution

    |

  16. Prove that the relation R defined on the set of real numbers R as R = ...

    Text Solution

    |