How many satisfying assignments are there in a set of 3-CNF clauses where no clause share the same variable?

Question

Maybe a little outside the scope of this site, but I figured enough people here would know this so that I am giving it a shot.

Say I have a set of 3-CNF clauses

 S = {Clause1, Clause2} = {<x1 or x2 or not x3>, <x4 or x5 or x6>}

Each variable range over {0,1}

How many satisfying assignments are there for S? In general, how many satisfying assignments are there for S is the size of S is k?

This is a question about what is a satisfying assignment for 3-disjunctive clause as much as it is about counting. For example when I just have , there are 2³ = 8 possible assignments:

(111),(011),(101),(110),(100),(010),(001),(000)

But which one of these are satisfying assignments?

Answer 1

For clauses that do not share any variables, the counting is pretty trivial.

For each set of variables satisfying the first clause, you can pick any set of variables satisfying the second clause. Thus you simply want the product of satisfying assignments of each of your clauses.