Philosophy Logic Assignment

[dekoi]

I was hesitant to post this thread in this specific forum. Although i do not think it would be appropriate in the more physics-centered Homework Help forum.

I am creating an outline (as well as a précis) for a short 10 minute presentation i have to have finished in a couple of days. The topic is Aristotle's Logic -- although it is a shortened version due to the time limit.

So far i have an introduction to what logic is and why it is important, Primary Rule of logic (law of non-contradiction), and descriptions/examples of Immediate Inference and Syllogistic Reasoning.

My question is: What other important aspects of Aristotle's Logic should i include in this presentation?

And while on the topic, would anyone have an understanding of what this equation means. It should be on the topic of logical assertion.

\vdash \left( (\vdash p)\rightarrow(p \pmod 2 \equiv 0) \right)

Thank you as always.

[dekoi]

\vdash \left( (\vdash p)\rightarrow(p \pmod 2 \equiv 0) \right)

... means :
\vdash \left( (\vdash p)\rightarrow 1-no \rightarrow yes
Therefore, left side = yes.
Now the right side, (p \pmod 2 \equiv 0) \right) is valid, since 'mod2' = 0 (mod'even'=0, mod'odd'=1 right?).

Am i correct with this information?

Sorry for bumping an old thread, but it has not been answered in many days.

As for, My question is: What other important aspects of Aristotle's Logic should i include in this presentation? I am still open for suggestions.