Home
Class 12
MATHS
Let L be the set of all lines in XY-pJan...

Let L be the set of all lines in XY-pJane and R be the relation in L defined as `R={(L_(1), L_(2)): L_(1)` is parallel to `L_2`}. Show that R is an equivalence relation. Find the set of all lines related to the line `y = 2x + 4`

Promotional Banner

Topper's Solved these Questions

  • RELATIONS AND FUNCTION

    MODERN PUBLICATION|Exercise EXAMPLE|212 Videos

  • PROBABILITY

    MODERN PUBLICATION|Exercise EXERCISE|543 Videos

  • RELATIONS AND FUNCTIONS

    MODERN PUBLICATION|Exercise EXAMPLE|13 Videos

Similar Questions

Explore conceptually related problems

Let L be the set of all lines in XY plane and R be the relation in L defined as R={(L_(1),L_(2)),L_(1) is parallel to L_(2)} . Show that R is an equilavence relation.

Let L be the set of all lines in the XY-plane and R be the relation in L defined by : R = {(l_i l_j) = l_i is parallel to l_j. Aai,j} Show that R is an equivalence relation. Find the set of all lines related to the y = 7x +5.

Let L be the set of all lines in the plane and R be the relation in L, defined as R = (L_1,L_2):L_1 is perpendicular to L_2) . Show that R is symmetric but neither reflexive nor transitive.

Let T be the set of all triangles in a plane with R a relation in T given by : R = {(T_1, T_2) : T_1 is congruent to T_2}. Show that R is an equivalence relation.

Show that relation R = {(L_1, L_2) : L_1 is parallel to L_2 }, defined on the set of all lines, is an equivalence relation.

Let L be the set of all lines in a plane and R be the relation on L defined as R = (l,m) : l is perpendicular to m). Check whether R is reflexive, symmetric or transitive.

Let S be the set of all real numbers and let R be the relation in S defined by R = {(a,b), a leb^2 }, then

Let Z be the set of all integers and R be the relation on Z defined as R = (a,b) : a,b in Z and a-b is divisible by 5) Prove that R is an equivalence relation.

Let N be the set of natural number and R be the relation in NxxN defined by : (a,b) R (c,d) iff ad = bc, for all (a,b), (c,d) in NxxN Show that R is an equivalence relation.

Show that the relation R defined in the set A of all triangles as R={(T_(1),T_(2)):T_(1) is similar to T_(2)} is an equivalence relation.

MODERN PUBLICATION-RELATIONS AND FUNCTION-EXAMPLE
  1. Show that the relation R, defined by the set A of all triangles as : R...

    Text Solution

    |

  2. Show that the relation R defined in the set A of all polygons as R = {...

    Text Solution

    |

  3. Let L be the set of all lines in XY-pJane and R be the relation in L d...

    Text Solution

    |

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

    Text Solution

    |

  5. Let R be the relation in the set N given by R = {(a, b) : a = b – 2, b...

    Text Solution

    |

  6. Show that the function f : R* rarr R* defined by f (x) = 1/x is one...

    Text Solution

    |

  7. Check the injectivity and surjectivity of the following function: f ...

    Text Solution

    |

  8. Check the injectivity and surjectivity of the following function: f :...

    Text Solution

    |

  9. Check the injectivity and surjectivity of the following function: f :...

    Text Solution

    |

  10. Check the injectivity and surjectivity of the following function: f ...

    Text Solution

    |

  11. Check the injectivity and surjectivity of the following function: f ...

    Text Solution

    |

  12. Prove that greatest integer function f: RrarrR, given by f (x) = [x], ...

    Text Solution

    |

  13. Prove that Modulus Function f: R rarr R given by : f(x) = | x | is nei...

    Text Solution

    |

  14. Show that the signum function f : R to R given by: f(x) = {{:(1, if ...

    Text Solution

    |

  15. Let A = {1, 2, 3}, B = {4, 5, 6, 7} and let f = {(1, 4), (2, 5), (3, 6...

    Text Solution

    |

  16. In the following case, state whether the function is one-one, onto or ...

    Text Solution

    |

  17. Let A and B be sets, show that f : A xx B rarr B xx A such that f(a,b...

    Text Solution

    |

  18. Let f: N to N be defined by f(n) = {{:((n+1)/2, " if n is odd "),(n/2,...

    Text Solution

    |

  19. Let A =R-{3} and B=R-{1}. Consider the function f : A to B defined by ...

    Text Solution

    |

  20. Let f : R rarr R be defined as f(x) = x^4. Choose the correct answer.

    Text Solution

    |