How to find if a valuation satisfies a statement? I'm working on a task which i'm a bit stuck at. I need to decide whether the statements are true or fale. F stands for the statement logical formulas, and also if the claim is true I need to give a proof or explain why it is so. If the statement is false I need to give a contra-example
Here are the statements:

For all F, then F is satisfiable or ¬F is satisfiable

and

For all F, then F is valid or ¬F is valid.

Is there any easy way I can solve these kinds of statements by seeing if a statement satisfies or is valid or is neither both of them?
Would appreciate some help, thanks alot!
 A: There exist three classes of formulas: tautologies, contingencies, and contradictions.  A tautology has all "1"'s (at the end of its rows) for its truth table, a contingency has at least one "1" and at least one "0" for its truth table, and a contradiction has all "0"'s for its truth table.
Case 1:  If a formula F qualifies as a tautology, it qualifies as valid.  Thus, it always comes as satisfied, and thus always satisfiable.  So, if F qualifies as a tautology, then either F is satisfiable or $\lnot$F is satisfiable.  
Case 2: If a formula F qualifies as a contingency, then its truth table has at least one row with a "1" in it.  Consequently, for that row the formula gets satisfied and thus F qualifies as satisfiable.  So, if F qualifies as a contingency, then either F is satisfiable or $\lnot$F is satisfiable.
Case 3: If a formula F qualifies as a contradiction, then it has all "0"'s in its truth table.  So, for no row does it come as satisfied.  Thus, $\lnot$F has all "1"'s for its truth table.  So, $\lnot$F always qualifies as satisfied, and thus qualifies as satisfiable.  So, if F qualifies as a contradiction, then either F is satisfiable or $\lnot$ F is satisfiable.
Since these cases exhaust the possibilities, for any given propositional formula F either F is satisfiable or $\lnot$F is satisfiable.
As Git Gud points out you only need to consider a truth table for a propositional atom for the second part.
