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If A={2,\ 3,\ 4} , B={1,\ 3,\ 7} and R={...

If `A={2,\ 3,\ 4}` , `B={1,\ 3,\ 7}` and `R={(x ,\ y): x in A ,\ y in B\ a n d\ x

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The correct Answer is:
`R={(2,3),(2,7),(3,7),(4,7)}`
`{R}^{-1}={(3,2),(7,2),(7,3),(7,4)}`

Now, R is defined from A to B, where A is domain/ input set
And B is codomain/output set

So` R^(-1) `can be simply defined as B to A
Where roles of A and B are replaced from input to output and vice-versa.
Most simple method for finding R is by checking each pair.

In this case `R^(-1)` can also be defined as xRy : x>y

...
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RD SHARMA-RELATIONS-Solved Examples And Exercises
  1. If R is a symmetric relation on a set A , then write a relation betwee...

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

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

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

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  5. Define a reflexive relation.

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  6. Define a symmetric relation.

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  7. Define a transitive relation.

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  8. Define an equivalence relation.

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  9. If A={3,\ 5,\ 7} and B={2,\ 4,\ 9} and R is a relation given by is les...

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  10. A={1,\ 2,\ 3,\ 4,\ 5,\ 6,\ 7} and if R={(x ,\ y): y is one half of x ;...

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  12. State the reason for the relation R on the set {1, 2, 3} given by R={(...

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  14. Let R be the relation in the set Z of integers given by R={(a,b):2 div...

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  15. For the set A={1,\ 2,\ 3} , define a relation R on the set A as follow...

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  16. Let A={0,\ 1,\ 2,\ 3} and R be a relation on A defined as R={(0,\ 0),\...

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  17. If the relation R be defined on the set A={1,2,3,4,5} by R={(a,b): |a^...

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  18. Let the relation R be defined in N by aRb, if 2a + 3b = 30. Then R = …...

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  19. Write the smallest equivalence relation on the set A={1,\ 2,\ 3} .

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  20. Let R be a relation on the set N given by R={(a ,\ b): a=b-2,\ b >6}do...

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