Building a recursive string function.

I am trying to build a function whose output is a list of all possible boolean expressions with an upper bound. For three variables p,q and r my function would be, theoretically:

1. f(0) = {p,q,r} // this notation refer to the mathematical set such that p,q and r belong to f(0).
2. f(n+1) = { (A & B) such that A and B belongs to f(n) } Union { (A or B) such that A and B belongs to f(n) } Union { (not A) such that A belongs to f(n) }

I want to receive a matrix whose rows are the strings of all the possible strings corresponding to boolean formulas build by n iterations of the function. For example:

f(2)=['p' ; 'q' ; 'r' ; '(p&q)' ; 'p&(p or q)' ; 'r or (p & r)' ; ... ]

[José-Luis]

What have you tried so far?