Home
Class 12
MATHS
If R(1) and R(2) are equivalence relatio...

If `R_(1)` and `R_(2)` are equivalence relations in a set A, show that `R_(1) nn R_(2)` is also an equivalence relation.

Text Solution

Verified by Experts

The correct Answer is:
`R_(1) nn R_(2)` 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

Let R_1 and R_2 be two equivalence relations in the set A. Then:

Let R be a relation on a set A such that R= R^(-1) . Then R is :

Solve that the relation R in the set z of intergers given by R={(x,y):2 divides (x-y)} 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 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.

In the set of integers Z, which of the following relation R is not an equivalence relation?

Statement-1: The relation R on the set N xx N defined by (a, b) R (c, d) iff a+d = b+c for all a, b, c, d in N is an equivalence relation. Statement-2: The intersection of two equivalence relations on a set A is an equivalence relation.

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

    |