Finding Expressively Adequate truth Functions 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
 A: You are absolutely right : the exact number is 56, and it can be shown rigorously as follows.
By Post’s theorem, a boolean function is not expressively adequate iff it is either monotone, affine over $\frac{\mathbb Z}{2\mathbb Z}$, self-dual, truth-preserving or falsity-preserving.
In three variables this simplifies considerably. Indeed, not being truth- or falsity-preserving reduces to $f(0,0,0)=1$ and $f(1,1,1)=0$. Then $f$ is never monotone.  
We now partition the remaining set of functions into four subsets indexed by $\lbrace 0,1 \rbrace^2$ : for $a,b$ in $\lbrace 0,1 \rbrace$, put
$$
G_{a,b}=\lbrace f | f(0,0,0)=1, f(1,1,1)=0, f(0,0,1)=a, f(0,1,0)=b\rbrace
$$
Each $G_{a,b}$ contains a unique affine map (explicitly, $f(x,y,z)=1+ax+by-(a+b)z$ modulo 2). This affine map is always self-dual, and $G_{a,b}$ contains exactly two self-dual maps. Finally, each $G_{a,b}$ contains two nonadequate functions, and hence $2^4-2=14$ adequate functions, which makes a total of $2^2\times (2^4-2)=56$.
