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Show that the relations `R` on the set `R` of all real numbers, defined as `R={(a ,\ b): alt=b^2}` is neither reflexive nor symmetric nor transitive.

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RD SHARMA ENGLISH-RELATIONS-All Questions
  1. Let S be the set of all points in a plane and R be a relation on S def...

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  2. Let X={1,\ 2,\ 3,\ 4,\ 5,\ 6,\ 7,\ 8,\ 9} , Let R1 be a relation on X ...

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

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  4. Let A={1,\ 2,\ 3} . Then, show that the number of relations contain...

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  5. Let A be the set of all human beings in a town at a particular time...

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  6. Let A be the set of all human beings in a town at a particular time...

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  7. Let A be the set of all human beings in a town at a particular time...

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  8. Let A be the set of all human beings in a town at a particular time...

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  9. R1={(a ,\ a),\ (a ,\ b),\ (a ,\ c),\ (b ,\ b),\ (b ,\ c),\ (c ,\ a),\ ...

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  10. R2={(a ,\ a)} is defined on set A={a ,\ b ,\ c} . Find whether or not ...

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  11. R={(b , c)} is defined on set A={a ,\ b ,\ c} . Find whether or not it...

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  12. Test whether, R1 on Q0 defined by (a ,\ b) in R1<=> a=1//b is (i) ref...

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  13. Test whether, R2 on Z defined by (a ,\ b) in R2<=>|a-b|lt=5 is (i) re...

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  14. Test whether, R3 on R defined by (a ,\ b) in R3<=> a^2-4\ a b+3b^2=0 ...

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  15. Find whether or not R1={(1,\ 1),\ (1,\ 3),\ (3,\ 1),\ (2,\ 2),\ (2,\ 1...

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  16. Find whether or not R2={(2,\ 2),\ (3,\ 1),\ (1,\ 3)} , on A={1,\ 2,\ 3...

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  17. Find whether or not R3={(1,\ 3),\ (3,\ 3)} , on A={1,\ 2,\ 3} is (i) r...

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  18. a R b if a-b >0 is defined on the set of real numbers, find whether...

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  19. a R b iff 1+a b >0 is defined on the set of real numbers, find whet...

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  20. a R b if |a|lt=b is defined on the set of real numbers, find whethe...

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