De Morgan's Laws
In fact, all dual operators will interchange upon negation. So we can also say that for any proposition P, , because is dual with . Also, .
Any two propositions and have four possible combinations of truth values. We can therefore prove that two propositions stated in terms of and are equivalent by proving that they hold the same value in each of the four cases.
In the following truth table, indicates "true" and indicates "false".
Hence and .
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