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According to my textbook the implication P --> Q has the following truth table:

enter image description here

I don't understand the last two rows. For example in the last row, how can we determine P --> Q if all we know is that both P and Q is false. Shouldn't the truth value be unknown in that case?

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marked as duplicate by Henning Makholm logic May 31 '15 at 9:44

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  • $\begingroup$ Se also answers to this other instance of the question. $\endgroup$ – Henning Makholm May 31 '15 at 9:46
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    $\begingroup$ Or, perhaps even more on point, this one. $\endgroup$ – Henning Makholm May 31 '15 at 9:48
  • $\begingroup$ I'm sure this question has already been asked before on this website and there are also many google searches that will give you the answer to it. Try with YouTube, searching "logical connectives" (or PhiPsiPi). However, the easy way to understand this is noticing that when you assume something false to be true, there's no point in checking the truth of its consequences. In other words, it's okay to conclude anything from the hypothesis "cows can fly". $\endgroup$ – Jonathan Julián Huerta May 31 '15 at 9:53

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