Semantic method can be used to prove a certain wff is not a theorem. In this exercise students need to falsify a certain kind of wffs, namely all wffs without negation. You need to figure out two things:
- How to falsify them?
- How to prove through out all wffs?
Common Mistakes:
- Many students proved by induction on the length of the wff, which involves many unrigorous arguments. Remember, the best tool we have is The Principle of Induction on the Construction of a Wff.
- Many students were still using the arguments like ‘if the wff has has the form A\vee B, then blablabla’ or other unrigorous statements. Instead, you should use induction of the formation of wffs to prove your desired property on wffs.
- Two students tried to use syntactic approach. One of them almost succeeded except some minor mistakes. However, to refute a wff as a theorem, syntactic method usually makes things more complicated than the semantic way.