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` .

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The correct Answer is:

The set of all lines `y =2x +c, c in R`

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NCERT GUJARATI-RELATIONS AND FUNCTIONS -EXERCISE 1.1

Determine whether each of the following relations are reflexive, symm...
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Show that the relations R on the set R of all real numbers, defined as...
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Check whether the relation R defined in the set {1, 2, 3, 4, 5, 6}as R...
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Show that the relation R on R defined as R={(a ,\ b): alt=b} , is refl...
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Check whether the relation R in R defined by R={(a ,b):alt=b^3}is ref...
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Show that the relation R in the set {1, 2, 3}given by R = {(1, 2), (2,...
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Show that the relation R in the set A of all the books in a library...
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Show that the relation R on the set A={1,\ 2,\ 3,\ 4,\ 5} , given by R...
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Show that each of the relation R in the set A={x in Z :0lt=xlt=12}, ...
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Give an example of a relation. Which is (i) Symmetric but neither r...
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Show that the relation R on the set A of points in a plane, given by R...
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Show that the relation R defined on the set A of all triangles in a pl...
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Show that the relation R , defined on the set A of all polygons as R={...
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Let L be the set of all lines in X Y -plane and R be the relation in L...
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Let R be the relation in the set {(1,2,3,4} given by R ={(1,2), (2,2),...
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Let R be the relation in the set N given by R = {(a , b) : a = b 2, ...
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