Home
Class 12
MATHS
Let L be the set of all lines in X Y -pl...

Let `L` be the set of all lines in `X Y` -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 equivalence relation. Find the set of all lines related to the line `y=2x+4` .

Text Solution

Verified by Experts

The correct Answer is:
Set of all lines `y=2x+c, cinR`
Promotional Banner

Topper's Solved these Questions

  • RELATIONS AND FUNCTIONS

    MODERN PUBLICATION|Exercise EXERCISE 1 (b) (Long Answer Type Questions (I))|15 Videos

  • RELATIONS AND FUNCTIONS

    MODERN PUBLICATION|Exercise EXERCISE 1 (c) (Short Answer Type Questions)|7 Videos

  • RELATIONS AND FUNCTIONS

    MODERN PUBLICATION|Exercise EXERCISE 1 (a) (Long Answer Type Questions (I))|7 Videos

  • PROBABILITY

    MODERN PUBLICATION|Exercise MOCK TEST SECTION D|6 Videos

  • THREE DIMENSIONAL GEOMETRY

    MODERN PUBLICATION|Exercise CHAPTER TEST 11|11 Videos

Similar Questions

Explore conceptually related problems

Let L be the set of all lines in the plane and R be the relation in L, defined as : R = { (l_(i),l_(j))=l_(i) is parallel to l_(j),AA i,j }. Show that R is an equivalence relation. Find the set of all lines related to the line y=7x+5 .

Let A be the set of all lines in xy-plane and let R be relation in A , defind by R={(L_(1),L_(2)):L_(1)||L_(2)}. show that R is an equivalence relation in A. Find the set of all lines related to the line Y=3x+5.

Let L be the set of all lines in a 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 R be a relation on the set of all lines in a plane defined by (l_(1),l_(2))in R line l_(1) is parallel to line l_(2). Show that R is an equivalence relation.

Let R be a relation on the set of all line in a plane defined by (l_(1),l_(2))in R hArr l in el_(1) is parallel to line l_(2). Show that R is an equivalence relation.

Let L be the set of all lines in a plane and let R be a relation defined on L by the rule (x,y)epsilonRtox is perpendicular to y . Then prove that R is a symmetric relation on L .

Let R be a relation on the set Q of all rationals defined by R={(a,b):a,binQ" and "a-binZ}. Show that R is an equivalence relation.

Show that set of all parallel lines in any plane is an equivalence relation.

Let Z be the set of all integers. A relation R is defined on Z by xRy to mean x-y is divisible by 5. Show that R is an equivalence relation on Z.

Let Z be the set of all integers. A relation R is defined on Z by xRy to mean x-y is divisible by 5. Show that R is an equivalence relation on Z.