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

Let `S` be a relation on the set `R` of all real numbers defined by `S={(a ,\ b) in RxxR : a^2+b^2=1}` . Prove that `S` is not an equivalence relation on `R` .

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RD SHARMA ENGLISH-RELATIONS-All Questions
  1. Let O be the origin. We define a relation between two points P and ...

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  2. Let R be the relation defined on the set A={1,\ 2,\ 3,\ 4,\ 5,\ 6,\ 7}...

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

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  4. Let Z be the set of all integers and Z0 be the set of all non-zero int...

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

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

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

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  8. If R={(x ,\ y): x^2+y^2lt=4; x ,\ y in Z} is a relation on Z , write ...

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  9. Write the identity relation on set A={a ,\ b ,\ c} .

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  10. Write the smallest reflexive relation on set A={1,\ 2,\ 3,\ 4} .

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

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  12. If R is a symmetric relation on a set A , then write a relation betwee...

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

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  14. If A={1,2,\ 3,\ 4} , B={1,4,9,16,25} and R be a relation defined from ...

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

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  16. Define a reflexive relation.

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  17. Define a symmetric relation.

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  18. Define a transitive relation.

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  19. Define an equivalence relation.

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

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