How could I explain that the required amount of rows in a truth table of 4 different atomic sentences would be 16?
I know that the formula to express it is
2(possible values t, f) to the power of 4 = 16
What is the reasoning for this formula? Are possible variations involved here?
Each row in a truth table represents a different combination of truth values of the atomic sentences. Since each atomic statement is either true or false, the number of possibilities doubles for each atomic, so the number of possible combinations is $2^n$.
If you still don't see this, start with 1 atomic sentence. Now there are exactly 2 possibilities to consider: true or false. Ok, add another atomic sentence: for each of the previous two cases, you add the value of this new sentence, which can be true or false, so you have 2*2 possibilities. Ok, add a third. Again, to each of the 4 possibilities, you add another truth value, so you have 4 possibilities for the truth value combinations for the first two sentences with a true added for the third sentence, plus those same 4 possibilities for the first two sentences with a false added for the third, so that's 8. I think you now see how it doubles every time.