Question

# Is it true that every relation which is symmetric and transitive is also reflexive ? Give reasons.

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Hint: - If you have to check whether a relation is reflexive or not in this question , first you have to assume a relation which is symmetric and transitive both then you have to check for reflexive(that means you have to check the number is in relation with itself or not).

Clearly aRb $\Rightarrow$bRa that is if a and b are both odd then b and a are also both odd, so it is a symmetric relation.
But this relation is not reflexive because $2 \in {\text{I}}$ but it can’t be in relation with 2 that is with itself to be in reflexive relation, because 2 is even number, and condition for to be in relation is number has to be a odd number.