Home
Class 12
MATHS
Let A be the set of all students of a bo...

Let A be the set of all students of a boys school. Show that the relation R in A given by `R = {(a,b):a` is sister of b} is the empty relation and `R' ={(a,b):` the difference between heights of a and b is less than 3 meters } is the universal relation.

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

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

Show that the relation R in the set {1,2,3} given by R = {(1,2),(2,1)} is symmetric but neither reflexive nor transitive.

Show that the relation R is R defined as R = {(a,b) : a le b} is reflexive and transitive but not symmetric.

Check whether the relation R defined by R = {(a,b) : a le b^3} is reflexive , symmetric or transitive.

Let R be the relation on the set N given by R= { (a, b): a= b-2, b gt 6} . Choose the correct answer.

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

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 R be the relation on Z defined by R= {(a,b): a, b in Z, a-b "is an integer"). Find the domain and range of R.

Let R be a relation defined by R = {(a, b) : a ge b }, where a and b are real numbers, then R is

KUMAR PRAKASHAN-RELATIONS AND FUNCTIONS -Textbook Illustrations for Practice Work
  1. Let A be the set of all students of a boys school. Show that the relat...

    Text Solution

    |

  2. Let T be the set of all triangles in a plane with R a relation in T g...

    Text Solution

    |

  3. Let L be the set of all lines in a plane and R be the relation in L de...

    Text Solution

    |

  4. Show that the relation R in the set {1,2,3} given by R = {(1,1) ,(2,2)...

    Text Solution

    |

  5. Show that the relation R in the set Z of intergers given by R ={(a,...

    Text Solution

    |

  6. Let R be the realtion defined in the set A = {1,2,3,4,5,6,7} by R ={(a...

    Text Solution

    |

  7. Let A be the set of all 50 students of Class X in a school. Let f : A ...

    Text Solution

    |

  8. Show that the function f:N rarr N , given by f(x) = 2x, is one-one but...

    Text Solution

    |

  9. Prove that the function f :R rarr R , given by f(x) = 2x, is one-one a...

    Text Solution

    |

  10. Show that the function f:N rarr N , given by f(1) = f(2) = 1 and f(x) ...

    Text Solution

    |

  11. Show that the function f: R rarr R , defined as f(x) = x^2 , is neithe...

    Text Solution

    |

  12. Show that f:N rarr N , given by f(x) = {:{(x+1, " if x is odd"),(x-1...

    Text Solution

    |

  13. Show that an onto function f : {1, 2, 3} rarr {1, 2, 3} is always one...

    Text Solution

    |

  14. Show that a one-one function f : {1, 2, 3} rarr {1, 2, 3} must be ont...

    Text Solution

    |

  15. Let f: {2, 3, 4, 5} rarr {3, 4, 5, 9} and g : {3, 4, 5, 9} rarr {7, 1...

    Text Solution

    |

  16. Find gof and fog, if f:R rarr R and g: R rarrR are given by f(x) = c...

    Text Solution

    |

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

    Text Solution

    |

  18. Show that if f: A rarr B and g: B rarr C are one- one, then gof: A ra...

    Text Solution

    |

  19. Show that if f: A rarr B and g: B rarr C are onto, then gof: A rarr ...

    Text Solution

    |

  20. Consider functions f and g such that composite gof is defined and is o...

    Text Solution

    |