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Given the relation R={(1,\ 2),\ (2,\ 3)}...

Given the relation `R={(1,\ 2),\ (2,\ 3)}` on the set `A={1,\ 2,\ 3}` , add a minimum number of ordered pairs so that the enlarged relation is symmetric, transitive and reflexive.

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We have, $$ R=\{(1,2),(2,3)\} $$

`R` can be a transitive only when the elements `(1,3)` is added

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RD SHARMA-RELATIONS-Solved Examples And Exercises
  1. Give an example of a relation which is symmetric but neither reflex...

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  2. Give an example of a relation which is transitive but neither refle...

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  3. Given the relation R={(1,\ 2),\ (2,\ 3)} on the set A={1,\ 2,\ 3} , ad...

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  4. Let A={1,\ 2,\ 3} and R={(1,\ 2),\ (1,\ 1),\ (2,\ 3)} be a relation on...

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

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  7. Let R be a relation on the set of all lines in a plane defined by (l...

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  8. Show that the relation ‘is congruent to’ on the set of all triangle...

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  9. Show that the relation R defined on the set A of all triangles in a pl...

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

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  11. Show that the relation R on the set A of all the books in a library of...

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  12. Show that the relation R on the set A={1,\ 2,\ 3,\ 4,\ 5} , given by R...

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

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  14. Show that the relation R on the set A of points in a plane, given by R...

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  15. Prove that the relation R on the set NxxN defined by (a ,\ b)R\ <=>(c ...

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  16. Let A={1,\ 2,\ 3,\ ,\ 9} and R be the relation on AxxA defined by (a ...

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

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  18. Let N denote the set of all natural numbers and R be the relation on ...

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  19. Prove that the relation congruence modulo m on the set Z of all int...

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  20. Show that the number of equivalence relations on the set {1, 2, 3} ...

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