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I'm following a YouTube tutorial on propositional logic, but have noticed the following well formed formula example and I'm struggling to make sense of it: $$ \lnot [(A \lor B) \equiv (E\supset C)] $$

How should this be interpreted. At the moment - and I know this isn't right - I'm interpreting it is:

  • A or B is not equivalent to C if E is true.
  • So, C is not equivalent to A or B if E is true.

But I'm struggling with the $(A \lor B)$ being equivalent to C if E. It doesn't make sense to say A or B is equivalent to C, nor does the reverse seem right that C is equivalent to A or B.

R4D4
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    The formula "A or B" is not equivalent to the formula "if E, then C". – Mauro ALLEGRANZA Apr 20 '17 at 12:30
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    Formulating such things in natural language can be difficult. Mathematical language has parenthesis that natural language often lacks, overall natural language don't pay that much attention to the order of logical operations. – skyking Apr 20 '17 at 12:45

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