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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 ?

Answer»

Solution :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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