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I was wondering if someone could help me count the total number of Truth Functions of 3 variables, that can generate all the possible truth functions..

I got 56 but I'm not sure of the answer.

EDIT: Would just like to add that the functions have 3 variables but still have binary inputs and outputs. Also each function has a unique truth table

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    How did you get that?2012-03-29
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    I've merged your duplicate accounts. If you register your account, then your edits to your own question will not require review by a higher rep user.2012-03-30
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    @draks Well the truth functions of 2 variables, that generate all the other truth functions are joint denial (NOR) and alternative denial(NAND). Suppose that I have a 3-variable function f(X,Y,Z) which can generate all truth functions. Then I assumed that there should be at least a pair (X,Y) of the variables X,Y,Z such that when X=Y, f(X,X,Z) gives a 2-variable generative truth function i.e NOR or NAND. Then by using the Inclusion–exclusion principle, I found it to be 56... Although I'm not too sure that my assumptions and calculations are correct2012-03-30

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