Truth tables and necessary truths

In the essay Validity and necessary truths I used truth tables with necessary truths and impossibilities in it. I did it like this: P □Q P→□Q T T T F T T Note that the modal operator is placed in the truth table also. It could also be done like this: P Q P→Q T T T F T T Note that Q is true on all rows. When thinking about a necessary truth or an impossibility we can simply choose only to look at the rows where the proposition is true. The truth table above is a part of this larger truth table: P Q P→Q T T T T F F F T T F F T We simply only looked at rows 1 and 3.