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Let R be a relation on the set of all li...

Let `R` be a relation on the set of all line in a plane defined by `(l_1, l_2) in R i` is parallel to line `l_2dot` Show that R is an equivalence relation.

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RD SHARMA-RELATIONS-Solved Examples And Exercises
  1. Let N denote the set of all natural numbers and R be the relation on N...

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  2. Let N be the set of all natural numbers and let R be a relation on N×N...

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  3. Let R be a relation on the set of all line in a plane defined by (l1, ...

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  4. Each of the following defines a relation on N: x -> y , (i) x , y in ...

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  5. Let A={a , b , c) and the relation R be defined on A as follows: R={(a...

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  6. Given the relation R={(1,2),(2,3) on the set A={1,2,3}, add a minimum ...

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  7. Let A={1,2,3,.....,9} and R be the relation in AxxA defined by (a ,b)R...

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  8. Prove that the relation R on the set NxxN defined by (a ,\ b)R\ (c ,\ ...

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  9. Let n be a positive integer. Prove that the relation R on the set Z o...

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  10. Let "T" be the set of all triangles in a plane with "R" as relation ...

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

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

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

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

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  15. Let R be the equivalence relation in the set A={0,1,2,3,4,5} given ...

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

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  17. Let Z be the set of all integers and R be the relation on Z defi...

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  18. The union of two equivalence relations on a set is not necessarily an ...

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  19. Let A be the set of all students of a boys school. Show that the re...

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  20. Prove that a relation R on a set A is symmetric iff R=R^(-1) .

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