# Proving Boolean Functions

Please check my answer to this question and give me feedback . Question: Either exhibit 333 different boolean functions on the three variables p,q,r, or prove that there aren't 333 different such functions. My Answer: -For three variables p,q,r it will not produce 333 boolean functions because in according to the formular for “the number of boolean functions” that is 2^{(2^{n})} .Therefore 3 variables, we will end up with 256 different boolean functions and that is 2^{2^{3}}=256 boolean functions.

That is correct, there are $2^{2^3} = 2^8 = 256$ different truth tables on three Boolean variables. A truth table on $n$ variables has $2^n$ rows, and each row has two possible values: $0$ or $1$. So clearly there aren't $333$ unique Boolean functions on three Boolean variables.