I'm having trouble with a problem in Propositional Logic Using induction I am supposed to show that if a well formed formula (wff) X has no repetitions of sentence letters then X is invalid.
The hint in the back of the book says "Instead of trying to show directly that every wff without repetition of sentence letters has the feature of PL-invalidity, find some feature F that is stronger than PL-invalidity (i.e. some feature from which PL-invalidity follows), and prove that every wff has that feature."
What does invalidity follow from?
Show that every wff with no repeated sentence letters is satisfiable. This is pretty easy by using the disjunctive normal form. This implies that the negation of such a wff (which also has no repeated sentence letters) cannot be a tautology, i.e. it's invalid.