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Show that the relation `R` defined on the set `A` of all triangles in a plane as `R={(T_1,\ T_2): T_1` is similar to `T_2)` is an equivalence relation. Consider three right angle triangle `T_1` with sides `3,\ 4,\ 5;` `T_2` with sides `5,\ 12 ,\ 13` and `T_3` with sides 6, 8, 10. Which triangles among `T_1,\ T_2` and `T_3` are related?

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The correct Answer is:
`T _(1)` is related to `T _(3).`
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NCERT GUJARATI-RELATIONS AND FUNCTIONS -EXERCISE 1.1
  1. Determine whether each of the following relations are reflexive, symm...

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  2. Show that the relations R on the set R of all real numbers, defined as...

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  3. Check whether the relation R defined in the set {1, 2, 3, 4, 5, 6}as R...

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  4. Show that the relation R on R defined as R={(a ,\ b): alt=b} , is refl...

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  5. Check whether the relation R in R defined by R={(a ,b):alt=b^3}is ref...

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  6. Show that the relation R in the set {1, 2, 3}given by R = {(1, 2), (2,...

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

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

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  9. Show that each of the relation R in the set A={x in Z :0lt=xlt=12}, ...

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  10. Give an example of a relation. Which is (i) Symmetric but neither r...

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

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

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

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

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  15. Let R be the relation in the set {(1,2,3,4} given by R ={(1,2), (2,2),...

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  16. Let R be the relation in the set N given by R = {(a , b) : a = b 2, ...

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