Talk:Schröder Rule

Hey guys,

I need some major help on making this one up to scratch. I did the first half and I think the second will follow simply once that's right.

Any thoughts welcome :)

--Jshflynn (talk) 02:01, 8 March 2013 (UTC)

ProofWiki 101: First off it needs a rename. "The" has to go. --prime mover (talk) 06:18, 8 March 2013 (UTC)

Also, if you know the origin of the name, please post it using the "namedfor" template. Presumably it's Ernst Schröder? --prime mover (talk) 07:18, 8 March 2013 (UTC)

That's correct. Which would you like: "Schröder Rule" or "Schröder's Rule"? --Jshflynn (talk) 07:21, 8 March 2013 (UTC)

Well, which is it? If in your source work it's given as "The Schröder Rule" then use "Schröder Rule". In "also known as" we say it is usually known as with "The" in front of it. If we then find out it's referred to as "Schröder's Rule" we can add it as an "also known as".

I'm preparing a proof strategy. Your truth table approach looks fine to me, but what may be worth doing is extracting the propositional logic elements of this approach into a PropLog page in its own right, so we can add a second proof based on natural deduction: $(a \land b) \implies c \dashv \vdash \neg (a \land b) \lor c \dashv \vdash \neg a \lor \neg b \lor c$ etc.

The bit you glossed over is where you state without explicitly showing it that:

by the definition of inverse relation and the complement of a relation we have that statement $(2)$ may be written as:

$\forall x, y, z \in S: ((x, y) \in A \land (x, z) \notin C) \implies (y, z) \notin B$

This needs to be expanded.

Apart from that, the approach looks fine to me. --prime mover (talk) 07:37, 8 March 2013 (UTC)