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Determine whether each of the following relations are reflexive, symmetric and transitive:(i) Relation R in the set `A = {1, 2, 3, ..., 13 , 14}`defined as `R = {(x , y) : 3x y = 0}`(ii) Relation R in the set N o

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The correct Answer is:
(i) Neither reflexive nor symmetric nor transitive.
(ii) Neither reflexive nor symmetric but transitive.
(iii) Reflexive and transitive but not symmetric.
(iv) Reflexive, symmetric and transitive.
(v) (a) Reflexive, symmetric and transitive.
(b) Reflexive, symmetric and transitive.
(c ) Neither reflexive nor symmetric nor transitive.
(d) Neither reflexive nor symmetric but transitive.
(e) Neither reflexive nor symmetric nor transitive.
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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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