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Let T be the set of all triangles in the...

Let `T` be the set of all triangles in the Euclidean plane, and let a relation `R` on `T` be defined as `a\ R\ b` if `a` is congruent to `b` for all `a ,\ b in T` . Then, `R` is (a) reflexive but not symmetric (b) transitive but not symmetric (c) equivalence (d) none of these

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Let L denote the set of all straight lines in a plane. Let a relation R be defined by l\ R\ m iff l is perpendicular to m for all, l ,\ m in L . Then, R is (a) reflexive (b) symmetric (c) transitive (d) none of these

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RD SHARMA ENGLISH-RELATIONS-All Questions
  1. Let R={(a ,\ a),\ (b ,\ b),\ (c ,\ c),\ (a ,\ b)} be a relation on set...

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

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  3. If R is the largest equivalence relation on a set A and S is any relat...

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  4. If R is a relation on the set A={1,\ 2,\ 3,\ 4,\ 5,\ 6,\ 7,\ 8,\ 9} gi...

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  5. If R is a relation on the set A={1,\ 2,\ 3} given by R={(1,\ 1),\ (2,\...

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  6. If A={a ,\ b ,\ c ,\ d}, then a relation R={(a ,\ b),\ (b ,\ a),\ (a ,...

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  7. If A={1, 2, 3} , then a relation R={(2,3)} on A is (a) symmetric and t...

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  8. Let R be the relation on the set A={1,\ 2,\ 3,\ 4} given by R={(1,\ 2)...

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  9. Let A = {1, 2, 3}. Then number of equivalence relations containing (1...

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  10. The relation R={(1,\ 1),\ (2,\ 2),\ (3,\ 3)} on the set {1, 2, 3} is (...

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  11. S is a relation over the set R of all real numbers and it is given by ...

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  12. In the set Z of all integers, which of the following relation R is not...

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  13. Let A={1,\ 2,\ 3} and consider the relation R={(1,\ 1),\ (2,\ 2),\ (3,...

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  14. The relation S defined on the set R of all real number by the rule a\ ...

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  15. The maximum number of equivalence relations on the set A = {1, 2, 3} a...

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  16. Let R be a relation on the set N of natural numbers defined by n\ R\ m...

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  17. Let L denote the set of all straight lines in a plane. Let a relati...

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  18. Let T be the set of all triangles in the Euclidean plane, and let a...

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  19. Let R be a relation defined by R={(a, b): a >= b, a, b in RR}. The rel...

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  20. For real numbers x and y, we write x* y, if x - y +sqrt2 is an irratio...

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