Reasoning with sets

Key Ideas:

• Introducing Venn Diagrams

Visualizing Sets:

We've introduced a lot of notation so let's take a moment and consolidate all of this by using visual aids. You will encounter Venn diagrams during your study of sets.

You can easily express the various operations we showed in the previous section. Here is an intersection:

And here is a substraction:

How would you express the relationship between the three sets displayed in this diagram?

Take at least 3 minutes to think through it - what did you find?

There are a few different ways to express the relationship here, but the simples we could think of is: $(B \cap C) \cup (C \cap \bar A)$. Is it equivalent to what you found?

References:

For further details, you can read through the following chapters:

• A Concise introduction to logic part 1.9
• Discrete mathematics - an open introduction part 0.2