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I have a question where I have to show that the third statement is not a logical consequence of the 1st two using a truth table. I've seen how you'd do if there are only two (How to prove logical consequence?) statements but how do I do it in this case:

A. All actors and journalists invited to the party are late. B. There is at least a person who is on time. C. There is at least an invited person who is neither a journalist nor an actor.

Formalize the sentences and prove that C is not a logical consequence of A and B.

I was able to formalize these, but not sure where to go from here: formula for sentences

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  • $\begingroup$ C is a logical conclusion if you assume everyone who came to the party was invited. But if uninvited people can go to the party there could be that all the invited guests were actors and journalists (who were late) and the only people on time were uninvited (and we have no reason to assume they are or are not actors or journalists.) $\endgroup$
    – fleablood
    Commented Jan 26, 2019 at 2:31
  • $\begingroup$ @fleablood Thanks! I get that, but how can I show it using a truth table? I think I should've been more specific that I have to show it using a truth table. $\endgroup$
    – Gurvinder Singh
    Commented Jan 26, 2019 at 2:38

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