I need to proof that if formula F in CNF form is satisfiable, then any subset of CNF which belongs to F must be satisfiable. I know that CNF is basically conjuncted sets of disjunctions so from definition it is kind of obvious that if whole formula in CNF is satisfiable, then any subset will definitely be satisfiable as well because any subset will have an interpretation which will be True. However, I am not sure how to start to proof it formally.
Yeah, it is kind of obvious ... to make it hard, I would say: if $F$ is satisfiable, then that means that there is some truth-value assignment that sets all of the conjuncts of its CNF to true. So, that verysame truth-value assignment will certainly set any subset of those conjuncts to true, meaning that that set is satisfiable.