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Question

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

A
R is reflexive and hence an equivalence relation
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B
R is reflexive and hence a partial order
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C
R is reflexive and hence not an equivalence relation
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D
None of the above
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Solution

## The correct option is D None of the aboveA relation which is symmetric and transitive, need not be reflexive relation. (i) R={}: on the set A={a,b}. The relation R is symmetric and transitive but not reflexive. (ii) R={(a,a).(b,b)}; on the set A={a,b} The relation R is symmetric, transitive and also reflexive. ∴ A relation is transitive and symmetric relation but need not be reflexive relation.

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