1. L-strings & WFF

Beginning: The intersection of all good sets of L-strings is exactly equal to WFF.

Middle:

Prove that all intersections of S are a subsection of WWF and that all WFF is a subsection of S.

A is inside of B, all the elements in A are elements of B; to prove they are equal show that B is a subset of A

It is possible that S contains characters that are not possible in a WWF. This can happen as long as S starts with the atomic formulas. Each of the sets is closed so applying a WFF function to one proposition then falls in the set. All propositions are linked by WFF so WFF are subsets of S.

2. Why is this weird? There is something odd about our use of sets, intersections, and other mathematical entities in the previous problem. Discuss the issue and propose a resolution.

The above proof involves aspects of set theory, something we have not covered in detail. We are trying to build from the base up, but automatically you need more knowledge on the subject.