Partial ordering

[reddog843]

Prove that the inverse of a partial ordering is also a partial ordering.

[HallsofIvy]

You might want to start by reviewing the DEFINITIONS of "partial order" and "inverse of an order".

[Epsilon=One]

Please do not post the same question multiple times. (In referece to reddog843 duplicate post)Duplicate post deleted.

Thanks for concern.

[HallsofIvy]

reddog843 seems to have given up!

The original post was "Prove that the inverse of a partial ordering is also a partial ordering."

And I suggested "You might want to start by reviewing the DEFINITIONS of "partial order" and "inverse of an order"".

Since we haven't heard from reddog843 in some time, I will answer my own questions. A relation, aRb is a partial ordering if and only if, any time we have aRb and bRc, we also have aRc (the "transitive" property). A relation R' is the inverse of a relation R if and only if whenever aRb, we also have bR'a and whenever aR'b, we have bRa.

To prove that the inverse of a partial ordering (transitive relation) R, R', is also a partial ordering, suppose aR'b and bR'C. Then bRa and cRb. But that is the same as saying "cRb and bRa". Since R is transitive, cRa from which aR'c follows.

[Epsilon=One]

...I will answer my own questions.Often, this is the best, if not only, method of finding an intelligent, topical question to reply to.