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Give an example of a relation on the reals that is reflexive and symmetric, but not...

Give an example of a relation on the reals that is reflexive and symmetric, but not transitive

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Answer #1

Consider a relation on the set of real numbers such that :

Now,

  • If we consider, for then, . Therefore, the relation is reflexive.

Next,

  • If ,

Therefore the relation is symmetric.

But

  • But, if we take

Therefore, the relation is not transitive.

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