MathCastle
Proof Writing & Problem SolvingSuperchallenge

Proof Writing & Problem Solving · Superchallenge problem

Using only the letters PP and QQ, parentheses, and the connective ⇒\Rightarrow (as many times as you like), one can build statements such as P⇒(Q⇒P)P \Rightarrow (Q \Rightarrow P) or (P⇒Q)⇒Q(P \Rightarrow Q) \Rightarrow Q. Two statements count as the same if they have the same truth table. How many different truth tables can be produced?

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