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Show whether the following is true or false:

α |= β or β |= α, for any two formulas α and β

I'm assuming here that α and β are formulas, not a set of formulas. My thought is that I can prove that it is false if I show α doesn't entail β and β doesn't entail α. I tried using a truth table to help me with this problem, but it didn't seem to help. I'm not sure how to go about this problem. Any help will be appreciated.

  • 1
    Obviously not; consider p as α and q as β. – Mauro ALLEGRANZA Dec 6 '17 at 7:29
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    Already asked and answered in MSE. – Mauro ALLEGRANZA Dec 6 '17 at 7:33
  • Sorry, why does setting α and β as new variables make it clearer? – Amous Dec 6 '17 at 7:34
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    You have only to use truth table to check that neither p ⊨ q nor q ⊨ p, as already answered to your question in MSE. – Mauro ALLEGRANZA Dec 6 '17 at 8:39

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