Hello ktmr

I'm not sure about the meaning of the word 'different' in the phrase 'acan be reproduced by writing the letters ofbin a different order'. If the order is strictly different, then the relation is not reflexive, since if we re-arrange the order of the letters making up the wordathen we cannot reproduce the same wordaagain.

The relation is definitely symmetric (ifbcan be re-arranged to forma, thenacan be re-arranged to formb).

But the same problem over the interpretation of 'different' will apply to transitivity, sinceaRbandbRadoes not implyaRa, as it will need to if the relation is to be transitive.

However, if a 'different' order of the letters can actually mean leaving the letters in the same order, then the relation is reflexive, symmetric and transitive, and is therefore an equivalence.

Grandad