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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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We have, L is the set of lines.

`R=\{(L_{1}, L_{2}): L_{1}`. is parallel to `L_{2}\}` be a relation on L

Now,

...
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RD SHARMA-RELATIONS-Solved Examples And Exercises
  1. Let R be a relation on the set A of ordered pairs of integers defined ...

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  2. Show that the relation R on the set A={x in Z ;0lt=xlt=12} , given by...

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  3. Let L be the set of all lines in X Y -plane and R be the relation in L...

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  4. Show that the relation R , defined on the set A of all polygons as R={...

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  5. Let O be the origin. We define a relation between two points P and ...

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  6. Let R be the relation defined on the set A={1,\ 2,\ 3,\ 4,\ 5,\ 6,\ 7}...

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  7. Let S be a relation on the set R of all real numbers defined by S={(a ...

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  8. Let Z be the set of all integers and Z0 be the set of all non-zero int...

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  9. If R and S are relations on a set A , then prove the following: R and ...

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  10. If R and S are transitive relations on a set A , then prove that RuuS ...

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  11. Write the domain of the relation R defined on the set Z of integers as...

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  12. If R={(x ,\ y): x^2+y^2lt=4; x ,\ y in Z} is a relation on Z , write ...

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  13. Write the identity relation on set A={a ,\ b ,\ c} .

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  14. Write the smallest reflexive relation on set A={1,\ 2,\ 3,\ 4} .

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  15. If R={(x ,\ y): x+2y=8} is a relation on N , then write the range of R...

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  16. If R is a symmetric relation on a set A , then write a relation betwee...

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  17. Let R={(x ,\ y):|x^2-y^2|<1} be a relation on set A={1,\ 2,\ 3,\ 4,\ 5...

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  18. If A={2,\ 3,\ 4} , B={1,\ 3,\ 7} and R={(x ,\ y): x in A ,\ y in B\ ...

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  19. Let A={3,\ 5,\ 7} , B={2,\ 6,\ 10} and R be a relation from A to B def...

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  20. Define a reflexive relation.

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