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28 votes
28 votes

Let $R$ be a symmetric and transitive relation on a set $A$. Then

  1. $R$ is reflexive and hence an equivalence relation
  2. $R$ is reflexive and hence a partial order
  3. $R$ is reflexive and hence not an equivalence relation
  4. None of the above
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6 Answers

Best answer
41 votes
41 votes
The answer is $D$.

Let $A=\{1,2,3\}$ and relation $R=\{(1,2),(2,1),(1,1),(2,2)\}. R$ is symmetric and transitive but not reflexive. Because $(3,3)$ is not there.
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13 votes
13 votes
Answer: D

Let A = {(1,2),(2,1),(1,1)}

A is symmetric and transitive but not reflexive as (2,2) is not there.
8 votes
8 votes
here ans should be D

explanation:

here the relation is symmetric and transitive. if relation is symmetric and transitive then it need not necessariy be reflexive;i.e. it may or may not be reflexive. therefore ans is D
8 votes
8 votes
We can take an empty set { } which is both symmetric and and transitive but not reflexive because diagonal elememts are not present in the set so not reflexive.
Answer:

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