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Let  A = {1, 2, 3} and let R = {(1, 1), (2, 2), (3, 3), (1, 3), (3, 2), (1, 2)}.  Then  R is 
  • a)
    reflexive and symmetric but not transitive
  • b)
    reflexive and transitive but not symmetric
  • c)
    symmetric and transitive but not reflexive
  • d)
    an equivalence relation 
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
Let A = {1, 2, 3} and let R = {(1, 1), (2, 2), (3, 3), (1, 3), (3, 2),...
Solution:

  • Reflexive: R is not reflexive, since (2,2) and (3,3) are not in R.

  • Symmetric: R is not symmetric, since (1,2) is in R but (2,1) is not in R.

  • Transitive: R is transitive, since if (a, b) and (b, c) are in R, then (a, c) is also in R. For example, (1,3) and (3,2) are in R, so (1,2) must also be in R.


Since R is not reflexive or symmetric, it cannot be an equivalence relation. However, since R is transitive, it is reflexive and transitive but not symmetric, which corresponds to option B.
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Community Answer
Let A = {1, 2, 3} and let R = {(1, 1), (2, 2), (3, 3), (1, 3), (3, 2),...
It is not symmetric as the elements (3,1),(2,3) and (2,1) are missing But it is reflexive and transitive
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Let A = {1, 2, 3} and let R = {(1, 1), (2, 2), (3, 3), (1, 3), (3, 2), (1, 2)}. Then R isa)reflexive and symmetric but not transitiveb)reflexive and transitive but not symmetricc)symmetric and transitive but not reflexived)an equivalence relationCorrect answer is option 'B'. Can you explain this answer?
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