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Let R be a relation on X, If R is symmet...

Let R be a relation on X, If R is symmetric then `xRy impliesyRx`. If it is also transitive then xRy and `yRx implies xRx`.So whenver a relation is symmetric and transitive then it is also reflexive. What is wrong in this argument ?

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Let R is a relation on X.`
If R is symmetric the `xRy implies yRx`
If R is also transitive then xRy and yRx `impliesxRx`
` implies` Whenever a relation is symmetric and transitive , then it is reflexive.
This argument is wrong because the symmetry of R does not imply dom R does not imply domR =Xand for reflexive `xRx AA x in X`.
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