In article <email@example.com>, <firstname.lastname@example.org> wrote:
>I am kinda new to discrete mathematics. I am reading a book by Harry >Lewis, in which I find some confusing sentences. Here is one:
>a binary relation that is not reflexive but has a transitive closure that >is reflexive.
That is not a sentence. It has no verb. Are you saying there is some particular binary relation that has these properties? It certainly is not true of all binary relations.
>I understand 'reflexive', but just don't get 'transitive closure', and a >'transitive closure that is reflexive'. So confusing.
>Can you guys help explain this to me with an example? Thanks a lot.
Consider the not-equal relation R on any set X having at least two members. R is not reflexive, but its transitive closure R' is reflexive, because for each x in X there exists y in X such that xRy and yRx (meaning x != y and y != x). Hence (x,x) is in R', the transitive closure of R.
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