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Let R be the relation on the set A={1,\ ...

Let `R` be the relation on the set `A={1,\ 2,\ 3,\ 4}` given by `R={(1,\ 2),\ (2,\ 2),\ (1,\ 1),\ (4,\ 4),\ (1,\ 3),\ (3,\ 3),\ (3,\ 2)}` . Then, `R` is reflexive and symmetric but not transitive (b) `R` is reflexive and transitive but not symmetric (c) `R` is symmetric and transitive but not reflexive (d) `R` is an equivalence relation

A

R is reflexive and symmetric but not transitive

B

R is reflexive and transitive but not symmetric

C

R is symmetric and transitive but not reflexive

D

R is an equivalence relation

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The correct Answer is:
B
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MODERN PUBLICATION-RELATIONS AND FUNCTIONS-Objective Type Questions (A. Multiple Choice Questions)
  1. Let R be the relation on the set A={1,\ 2,\ 3,\ 4} given by R={(1,\ 2)...

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

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  3. LetA = {1, 2, 3}Then number of relations containing (1, 2) a n d (1, 3...

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

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  5. Let f: R->Rbe defined as f(x)=x^4. Choose the correct answer. (A) f i...

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  6. Let f:RrarrR be defined as f(x)=3x. Then :

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  7. If f:RrarrR be given by f(x)=(3-x^(3))^(1//3), then fof(x) is :

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  8. Let f: R-{5/4}->R be a function defines f(x)=(5x)/(4x+5). The invers...

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  9. Consider a binary operation '**' on N defined as : a**b=a^(3)+b^(3). T...

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  10. Number of binary operations on the set {a, b} are (A) 10 (B) 16 (C)...

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

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  12. Set A has 3 elements and the set B has 4 elements. Then, the number of...

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  13. Let f:RrarrR be defined by f(x)=sinx and g:RrarrR be defined by g(x)=x...

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  14. Let f:RrarrR be defined by f(x)=x^(2)+1. Then pre-images of 17 and - 3...

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  15. Let f:RrarrR be defined by : f(x)={(2x,,xgt3),(x^(2),,1ltxlt3),(3x,,...

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  16. If f(x)=logx and g(x)=e^(x), then (fog) (x) is:

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  17. If f(x)=|x|andg(x)=x-2, then gof is equal to:

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  18. Consider the set Q with binary operation '**' as: a**b=(ab)/(4). The...

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  19. If f:RrarrR be given by f(x)=(3-x^(3))^(1//3), then f^(-1)(x) equals:

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  20. The number of one-one functions from a set containing 2 elements to a ...

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