Home
Class 12
MATHS
In the set of straight lines in a plane,...

In the set of straight lines in a plane, for the relation 'perpendicular' check whether it is reflexive, symmetric and transitive.

Text Solution

AI Generated Solution

To determine whether the relation 'perpendicular' among straight lines in a plane is reflexive, symmetric, and transitive, we will analyze each property step by step. ### Step 1: Check for Reflexivity A relation is reflexive if every element is related to itself. In the context of lines, this means that a line must be perpendicular to itself. - **Analysis**: No line can be perpendicular to itself because the angle between a line and itself is 0 degrees, and perpendicular lines must intersect at a right angle (90 degrees). - **Conclusion**: Since no line is perpendicular to itself, the relation 'perpendicular' is **not reflexive**. ...
Promotional Banner

Topper's Solved these Questions

  • RELATIONS AND FUNCTIONS

    NAGEEN PRAKASHAN|Exercise Exercies 1a|16 Videos
  • RELATIONS AND FUNCTIONS

    NAGEEN PRAKASHAN|Exercise Exercies 1b|18 Videos
  • PROBABIILITY

    NAGEEN PRAKASHAN|Exercise Miscellaneous Exercise|19 Videos
  • THREE-DIMENSIONAL GEOMETRY

    NAGEEN PRAKASHAN|Exercise Miscellaneous Exercise|23 Videos

Similar Questions

Explore conceptually related problems

aRb if a-b>0 is defined on the set of real numbers,find whether it is reflexive, symmetric or transitive.

aRb if |a|<=b is defined on the set of real numbers,find whether it is reflexive, symmetric or transitive.

aRb iff 1+ab>0 is defined on the set of real numbers,find whether it is reflexive, symmetric or transitive.

Give an example of a relation which is reflexive and symmetric but not transitive.

Explain the Relation (i) Reflexive (ii)Symmetric(iii) Transitive

Let Q be the set of rational number and R be the relation on Q defined by R={(x,y):x,y in Q , x^(2)+3y^(2)=4xy} check whether R is reflexive, symmetric and transitive.

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

NAGEEN PRAKASHAN-RELATIONS AND FUNCTIONS -Miscellaneous Exercise
  1. In the set of straight lines in a plane, for the relation 'perpendicul...

    Text Solution

    |

  2. Let f: R ->Rbe defined as f(x) = 10 x + 7. Find the function g: R ->R...

    Text Solution

    |

  3. Let f: W ->Wbe defined as f(n) = n - 1, if is odd and f(n) = n + 1, i...

    Text Solution

    |

  4. If f: R ->Ris defined by f(x) = x^2- 3x + 2, find f(f(x)).

    Text Solution

    |

  5. Show that the function f: R rarr { x in R: -1 lt x lt 1 } defined by ...

    Text Solution

    |

  6. Show that the function f: R->Rgiven by f(x)=x^3is injective.

    Text Solution

    |

  7. Give examples of two functions f:" "N->Z" "a n dg:" "Z->Z such that o...

    Text Solution

    |

  8. Given examples of two functions f:" "N ->N" "a n d""""""g:" "N->N such...

    Text Solution

    |

  9. Given a non-empty set X, consider P(X) which is the set of all subs...

    Text Solution

    |

  10. Given a non-empty set X, consider the binary operation *: P(X)xx P(X)...

    Text Solution

    |

  11. Find the number of all onto functions from the set {1, 2, 3, , n)to ...

    Text Solution

    |

  12. Let S = {a , b , c} a n d T = {1, 2, 3}. Find F^(-1)of the following ...

    Text Solution

    |

  13. Consider the binary operations*: RxxR->R and o: RxxR->R defined as ...

    Text Solution

    |

  14. Given a non -empty set X, let *:" "P(X)" "xx" "P(X) ->P(X) be defined ...

    Text Solution

    |

  15. Define a binary operation * on the set A={0,1,2,3,4,5} as a*b=a+b (mod...

    Text Solution

    |

  16. Let A" "=" "{-1," "0," "1," "2} , B" "=" "{-4," "-2," "0," "2} and f,g...

    Text Solution

    |

  17. LetA = {1, 2, 3}Then number of relations containing (1, 2) a n d (1, 3...

    Text Solution

    |

  18. Let A = {1, 2, 3}. Then number of equivalence relations containing (1...

    Text Solution

    |

  19. Let f: R->Rbe the Signum Function defined as f(x)={1,x >0 0,x=0-1,x<1 ...

    Text Solution

    |

  20. Number of binary operations on the set {a, b} are (A) 10 (B) 16 (C)...

    Text Solution

    |