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De Morgan's Laws

Proposition: For all formulas A and B, the following holds:

~(A /\  B) iff ~A \/ ~B,
~(A \/ B) iff ~A /\  ~B
Proof: by truth table.

Consequence: For all formulas A and B, we have:

A \/ B iff ~(~A /\  ~B).
Proof: by inversion of negation.

Disjunction can thus be defined by conjunction and negation.

Author: Wolfgang Schreiner
Last Modification: October 6, 1999

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