I've got a question:

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How many different (in the sense of calculating different truth-tables) functions are there in bool -> bool -> bool?

My answer to this question (which was wrong), was:

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Because of a possible result of only true and false, we can say that there are 2nc (2 to the power of the number of different combinations). For two variables we can have four combinations: a, a ̅, b and b ̅. Similarly if we have 4 variables, there are 2x2x2x2=24 combinations for them. Hence we can say there are 2n combinations between the variables. Therefore we get 2nc = 2^(〖(2〗^n)) combinations between them all.

Can anyone help explain as to why this is wrong? And maybe give me a better answer? Thanks!