course: Symbolic logic
Question: Prove by complete mathematical induction that any formula can be given a complete analytical tableau.
Hint: Work by mathematical induction on the degree of the formula. That is to say, prove that if any formula of degree less than or equal to n can be given a complete analytical tableau, any formula of degree n+1 can be given a complete analytical tableau. Thus, you should assume(1)that any formula of degree n+1. If X is unsigned, er can proceed via the fellowing three cases. Either:(a)X begins with a double negation; (b) X is an "alpha";or(C)X is a "beta".