Home
Class 12
MATHS
Let X = {1, 2, 3, 4, 5, 6, 7, 8, 9). Let...

Let X = {1, 2, 3, 4, 5, 6, 7, 8, 9). Let `R_1` be a relation in X given by `R_1 = {(x, y) : x - y` is divisible by 3} and R, be another relation on X given by `R_2 = {(x, y) : {x, y}sub {1, 4, 7}}` or `{x,y} sub{2,5,8} ` or `{x,y} sub {3,6,9}` . Show that `R_1 = R_2` .

Promotional Banner

Topper's Solved these Questions

  • RELATIONS AND FUNCTIONS

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

  • RELATIONS AND FUNCTIONS

    KUMAR PRAKASHAN|Exercise Solutions of NCERT Exemplar Problems (Long Answer Type Questions)|30 Videos

  • RELATIONS AND FUNCTIONS

    KUMAR PRAKASHAN|Exercise Textbook based MCQs|64 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

The relation R difined the set Z as R = {(x,y) : x - yin Z} show that R is an equivalence relation.

Determine the domain and range of the relation R defined by R={(x,x+5) : x in [0,1,2,3,4,5}} .

Let sets R and T be defined as R= {x in Z|x is divisible by 2} T= {x in Z| x is divisible by 6}. Then T sub R .

Write the following relation in roster from R= {(x,y): x in A, yin B . Y is divisible by x} where A= {5, 6,7, 8} B= {10, 12, 15, 16, 18}

Let X = {1, 2, 3, 4,5} and Y = {1, 3, 5, 7,9} . Which of the following is relations from X to Y

The ordered pair (5,2) belongs to the relation R= {(x,y): y= x-5, x, y in Z}

If R= {(x,y): x, y in W, x^(2)+ y^(2)= 25} , then find the domain and range of R.

A =(1, 2, 3, 5) and B= {4, 6, 9). Define a relation R from A to B by R= {(x, y): the difference between x and y is odd, x in A, y in B} . Write R in roster form.

A = {(1,2,3,......10} The relation R defined in the set A as R = {(x,y) : y = 2x} . Show that R is not an equivalence relation.

A= {1, 2, 3, 4, 5} R = {(x,y) ||x^(2)-y^(2) | lt 16} Find R.

KUMAR PRAKASHAN-RELATIONS AND FUNCTIONS -Textbook Illustrations for Practice Work
  1. Show that the VV: RxxR rarr R given by (a, b) rarr max {a, b} and th...

    Text Solution

    |

  2. Show that + : Rxx R rarr R and xx: R xxR rarr R are commutative binar...

    Text Solution

    |

  3. Show that **: RxxR rarr R defined by a^(**) b = a + 2b is not commuta...

    Text Solution

    |

  4. Show that addition and multiplication are associative binary operation...

    Text Solution

    |

  5. Show that ""^** : R xxR rarr R given by a^** b rarr a + 2b is not ass...

    Text Solution

    |

  6. Show that zero is the identity for addition on R and 1 is the identity...

    Text Solution

    |

  7. Show that -a is the inverse of a for the addition operation '+' on R...

    Text Solution

    |

  8. Show that -a is not the inverse of a in N for the addition operation...

    Text Solution

    |

  9. If R1 and R2 are equivalence relations in a set A, show that R(1) cap...

    Text Solution

    |

  10. Let R be a relation on the set A of ordered pairs of positive integers...

    Text Solution

    |

  11. Let X = {1, 2, 3, 4, 5, 6, 7, 8, 9). Let R1 be a relation in X given ...

    Text Solution

    |

  12. Let f: X rarrY be a function. Define a relation R in X given by R = {...

    Text Solution

    |

  13. Determine which of the following binary operations on the set R are as...

    Text Solution

    |

  14. Determine which of the following binary operations on the set R are as...

    Text Solution

    |

  15. Find the number of all one-one functions from set A = {1, 2, 3} to its...

    Text Solution

    |

  16. Let A = {1, 2, 3} Then show that the number of relations containing (1...

    Text Solution

    |

  17. Show that the number of equivalence relation in the set {1, 2, 3} cont...

    Text Solution

    |

  18. Show that the number of binary operations on {1, 2} having 1 as identi...

    Text Solution

    |

  19. Consider the identity function I(N) : N rarr N defined as I(N) (x) = ...

    Text Solution

    |

  20. Consider a function f : [0,(pi)/2]rarrR given by f(x) = sin x and g :...

    Text Solution

    |