I already know that SAT and 3-SAT are NP-complete. If in 3-SAT the Boolean expression should be divided to clauses,such that every clause contains at most (in the original problem it says exactly) three literals would it still be NP-complete?
I think the answer is yes but I'm not sure of my solution. I think the reduction will remain pretty much the same. We'll use SAT. For the clauses that contain 1,2 or literals we don't change anything. For the clauses that contain more that 3 literals we turn them into clauses with 3 literals like we did in the original 3-SAT.
Are my thoughts correct or am I missing something?