A) reflexive, symmetric but not transitive.
B) symmetric, transitive but not reflexive
C) an equivalence relation.
D) reflexive, transitive but not symmetric
Correct Answer: D
Solution :
Let R \[=\{(3,3),(5,5),(9,9),(12,12),(5,12),\]\[(3,9),(3,12),(3,5)\}\]be a relation on set \[A=\{3,5,9,12\}\] Clearly, every element of A is related to itself. Therefore, it is a reflexive. Now, R is not symmetry because 3 is related to 5 but 5 is not related to 3. Also R is transitive relation because it satisfies the property that if \[a\text{ }R\text{ }b\] and \[b\text{ }R\text{ }c\]then\[a\,R\,c.\]
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