Consider the following special case of Boolean satisfiability, that we will call k-variable Boolean satisfiability. Let k E N be a fixed parameter (e.g., k 42). In k-variable Boolean satisfiability, you are given a Boolean formula f (x1, ... , Xk) with exactly k variables. (Note that while the number of variables k is fixed, the formula may otherwise be of any total size.) Decide if either (a) k-variability Boolean satisfiability has a polynomial time algorithm, or (b) a polynomial time algorithm for $K$-variable Boolean satisfiability implies a polynomial time algorithm for (general) Boolean satisfiability