Now that we're up to speed (or back up to speed) on basic set concepts, we're going to look at methods for proving things about sets. There are several standard methods used that we'll go over this section's lectures.
Video Lectures
In this series of lectures, we're going to look at some of the common methods used to prove statements about sets starting with proofs about subsets. (lecture slides)
In this lecture, we're going to go over several examples of proofs proving that two set expressions are equal - all relying on the standard method of showing the two sets are subsets of each other.
Proofs about the empty set require some different techniques than the methods commonly used with non-empty sets since we can't reasonably start a proof with, "Let x be an element of the set . . ." when we know the set doesn't have any elements. (lecture slides)
We're going to wrap up our discussion of proofs involving sets by looking at a proof about an indexed collection of sets that "generalizes" the distributive property that we saw earlier.
