How do I show 3-SAT is decidable?

Question

Knowing that we have a Turing machine that can do anything a C program can do, how do I show 3-SAT is decidable?

I know 3-SAT is satisfiable if we can find boolean values for the literals so at least one clause is set to true.

I understand the definition of decidable is basically if we have an algorithm that decides every instance of the problem (3-SAT in this case).

I'm confused on how to combine this knowledge to show 3-SAT is satisfiable.

Answer 1

Let be 0 = false, 1 = true, f the boolean function. The following pseudocode s = 0 for x = 0 to 1 for y = 0 to 1 for z = 0 to 1 if f(x,y,z) = 1 then s = 1 next z next y next x return s returns 0/false if the formula isn't satisfiable, 1/true if is satisfiable.