Question

general example of a relation which is not reflexive but is symmetric and transitive relation(please don't give examples of sets,i know that...)

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Answer 1

Answer:

Note that if R is symmetric, then dom(R)=range(R)={b∣(∃a)aRb}. Hence, to get an example of a relation R on a set A that is transitive and symmetric but not reflexive (on A), there has to be some a∈A which is not R-related to any b∈A.