1.4 KiB
1.4 KiB
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DeMorgan's Laws
DeMorgan's laws express some fundamental equivalences that obtain between the Boolean connectives.
First Law
The negation of a conjunction is logically equivalent to the disjunction of the negations of the original conjuncts.
\lnot (P \land Q) \leftrightarrow \lnot P \lor \lnot Q
The equivalence is demonstrated with the following truth-table
P |
Q |
\lnot (P \land Q) |
\lnot P \lor \lnot Q |
|---|---|---|---|
| T | T | F | F |
| T | F | T | T |
| F | T | T | T |
| F | F | T | T ### Truth conditions |
The negation of a disjunction is equivalent to the conjunction of the negation of the original disjuncts.
\lnot (P \lor Q) \leftrightarrow \lnot P \land \lnot Q
P |
Q |
\lnot (P \lor Q) |
\lnot P \land \lnot Q |
|---|---|---|---|
| T | T | F | F |
| T | F | F | F |
| F | T | F | F |
| F | F | T | T |