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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