Home
Class 12
MATHS
Let A = {1,2,3.......9} and R be the rel...

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

Promotional Banner

Topper's Solved these Questions

  • RELATIONS AND FUNCTIONS

    KUMAR PRAKASHAN|Exercise Solutions of NCERT Exemplar Problems (Objective type Questions)|20 Videos

  • RELATIONS AND FUNCTIONS

    KUMAR PRAKASHAN|Exercise Solutions of NCERT Exemplar Problems (Fillers)|5 Videos

  • RELATIONS AND FUNCTIONS

    KUMAR PRAKASHAN|Exercise Solutions of NCERT Exemplar Problems (Short Answer Type Questions)|19 Videos

  • PROBABILITY

    KUMAR PRAKASHAN|Exercise Practice Paper - 13 (Section - D (Answer the following questions))|2 Videos

  • THREE DIMENSIONAL GEOMETRY

    KUMAR PRAKASHAN|Exercise PRACTICE PAPER -11|16 Videos

Similar Questions

Explore conceptually related problems

R is relation in N xxN as (a,b) R (c,d) hArr ad = bc . Show that R is an equivalence relation.

Let R be a relation on N xx N defined by (a,b) R(c, d) hArr a + d= b + c for all (a,b) (c,d) in N xx N show that, (a, b) R (a,b) for all (a, b) in N xx N

Show that the relation R defined by (a,b) R (c,d) implies a + d = b +c on the set N xxN is an equivalence relation.

Let N denote the set of all natural numbers and R be the relation on NxN defined by (a , b)R(c , d) a d(b+c)=b c(a+d)dot Check whether R is an equivalence relation on NxNdot

Let R be a relation on N xx N defined by (a,b) R(c, d) hArr a + d= b + c for all (a,b) (c,d) in N xx N show that, (a,b) R (c, d) rArr (c, d) R (a, b) for all (a, b) (c, d) in N xx N

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.

A relation R on the set of complex numbers is defined by z_1 R z_2 if and oly if (z_1-z_2)/(z_1+z_2) is real Show that R is an equivalence relation.

Let f: X rarrY be a function. Define a relation R in X given by R = {(a, b): f(a) = f(b)} . Examine whether R is an equivalence relation or not.

Let the relation R be defined in N by aRb , if 2a + 3b = 30 . Then , R = .............

Let R be a relation on the set A of ordered pairs of positive integers defined by (x, y) R (u, v) if and only if xv= yu. Show that R is an equivalence relation.

KUMAR PRAKASHAN-RELATIONS AND FUNCTIONS -Solutions of NCERT Exemplar Problems (Long Answer Type Questions)
  1. Let A = R - {3} , B = R - {1} . If f : A rarr B be defined f(x) = (x-2...

    Text Solution

    |

  2. Let A = [-1,1] . Then , discuss whether the following functions define...

    Text Solution

    |

  3. Let A = [-1,1] . Then , discuss whether the following functions define...

    Text Solution

    |

  4. Check the injectivity and surjectivity of the following function . f...

    Text Solution

    |

  5. Let A = [-1,1] . Then , discuss whether the following functions define...

    Text Solution

    |

  6. Each of the following defines a relation of N : x is greater than y...

    Text Solution

    |

  7. Each of the following defines a relation of N : x+y = 10 , x , y in ...

    Text Solution

    |

  8. Each of the following defines a relation of N : x. y is square of a...

    Text Solution

    |

  9. Each of the following defines a relation of N : x+4y =10 , x , y in ...

    Text Solution

    |

  10. Let A = {1,2,3.......9} and R be the relation in AxxA defined by (a,b)...

    Text Solution

    |

  11. Using the definition ,prove that the function F : AtoB is invertible ...

    Text Solution

    |

  12. Functions f,g:RtoR are defined ,respectively, by f(x)=x^2+3x+1,g(x)=2x...

    Text Solution

    |

  13. Functions f,g:RtoR are defined ,respectively, by f(x)=x^2+3x+1,g(x)=2x...

    Text Solution

    |

  14. Functions f,g:RtoR are defined ,respectively, by f(x)=x^2+3x+1,g(x)=2x...

    Text Solution

    |

  15. Functions f,g:RtoR are defined ,respectively, by f(x)=x^2+3x+1,g(x)=2x...

    Text Solution

    |

  16. Let ** be the binary operation defined on Q. Find which of the follow...

    Text Solution

    |

  17. Let ** be the binary operation defined on Q. Find which of the follow...

    Text Solution

    |

  18. Let ** be the binary operation defined on Q. Find which of the follow...

    Text Solution

    |

  19. Let ** be the binary operation defined on Q. Find which of the follow...

    Text Solution

    |

  20. If ** be binary operation defined on R by a**b = 1 + ab, AA a,b in R ....

    Text Solution

    |