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For the given relation R on a set S, det...

For the given relation R on a set S, determine which are equivalence relations : (i) S is the set of all rational numbers a R b iff a= b. (ii) S is the set of all real numbers iff : (I) `|a |= |b|` (II) `a ge b`.

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PRADEEP PUBLICATION-RELATIONS AND FUNCTIONS-EXERCISE
  1. Let A = (a,b,c) and R be the relation defined on A as follows R = (a,a...

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  2. Let A = (6,7,8,10), B = (2,4,5) a inA , b in B and R be the relation f...

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  3. For the given relation R on a set S, determine which are equivalence r...

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  4. For the given relation R on a set S, determine which are equivalence r...

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  5. For the given relation R on a set S, determine which are equivalence r...

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  6. In the following cases, for the given relation R on the set S, determi...

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  7. In the following cases, for the given relation R on the set S, determi...

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  8. For the given relation R on a set S, determine which are equivalence r...

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  9. Check whether the relation R defined in the set (1, 2, 3, 4, 5, 6) as ...

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  10. Show that R= {(a, b): a ge b} is reflexive and transitive but not sym...

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  11. Let A be the set of human beings living in a town at a particular time...

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  12. Given the relation R = {(1, 2), (2, 3)} on the set of natural numbers,...

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  13. Show that each of the relation R in the set A ={x in z : 0 le x le 12}...

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  14. Show that each of the relation R in the set A = {x in Z : 0 le x le 12...

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  15. Is inclusion of a subset in another, in the context of a universal set...

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  16. If R is a relation in N xx N, show that the relation R defined by (a, ...

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  17. If R is the relation in N xx N defined by (a, b) R (c,d) if and only i...

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  18. Show that the relation R defined by (a, b) R(c,d)implies a+d=b+c in...

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  19. Each of the following defines a relation R in N. x R y if xy is squa...

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  20. Each of the following defines a relation R in N. x R y if xy is squa...

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