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.

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