View source for FA19:Lecture 3 Set constructions

In this lecture, we introduced some of the basic [[set]] operations, and started discussing how to [[proof|prove]] things.

* [[SP19:Lecture 3 Set constructions|Last semester's notes]]
* [[Media:fa19-lec03-setproofs-slides.pdf|Lecture slides]]

= Set operations =

There are several ways to combine sets together; here we discuss three: the [[union]], [[intersection]] and [[set difference]].

== Union ==
{{:Union}}

== Intersection ==
{{:Intersection}}

== Set difference ==
{{:Set difference}}

== Power set ==
{{:Power set}}

= Proofs =

We started to prove the following claim:

{{Claim:A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C)}}

We showed two ways not to prove the claim: [[proof by example]] (using a picture) and [[proof by rewriting]] (using logical equivalences).

== Proof by example ==

{{Proof:A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C) bogus proof (by example)}}

== Proof by rewriting ==

{{Proof:A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C) (example of poor style)}}

== Correct proof ==

We will develop a good proof together in the next lecture.