Answer:
2^(2^n)
Step-by-step explanation:
You want to know how many different truth tables of compound propositions there are that involve n propositional variables p1 . . . pn.
Truth table
N propositional variables can give rise to 2^n compound propositions. Each of those can be true or false, so the truth table that describes them can have 2^(2^n) different forms.
Example
With 2 variables, 4 propositions can be formed. Each of those can be true or false, so the 16 possible truth tables are ...
TTTT, TTTF, TTFT, TTFF, TFTT, TFTF, TFFT, TFFF,
FTTT, FTTF, FTFT, FTFF, FFTT, FFTF, FFFT, FFFF
With 6 variables, there can be 18446744073709551616 possible different truth tables.
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