In this video we introduce binary data as a simple example of information, and show how apparently more-complex examples can be encoded as binary data.
This set of slides is split between two videos, to allow you space to think.
We start by introducing barbara, the simplest classical syllogism, and the proposition, "all a are b", known as universal affirmation. We briefly review Euler diagrams, and introduce Venn diagrams.
Once you have watched the video above, check your understanding by drawing a few Euler diagrams and the corresponding Venn diagrams, each for a universe with three predicates. How many different Euler diagrams can you draw for three predicates?
Once you've done that, you're ready for the next video.
In the second video, we return to discuss the relationship between Euler and Venn diagrams, and introduce some notation.
Having watched this video, you should be able to count how many different Euler diagrams there should be for three predicates. Can you draw them all?
You should also check you can recognise and name the following
symbols:
¬ ⋀ ⋁ ⊨ .
We use Venn diagrams to show that barbara is sound.
Our second syllogism requires a new form of proposition --
universal denial.
Introducing negation gives a new syllogism as an
instance of barbara.
We introduce the logic of negation.
Syllogisms for free! We see how some simple reasoning allows us to derive three more syllogisms.
Legacy recording from a lecture delivered in 2019— you can use this to check your understanding.
You should listen at least from 28m02 onwards, where I propose a problem for you to ponder.