What's the Disjunctive Normal form or a tautology with two variables P & Q
is it P̅Q̅ + P̅Q + PQ̅ + PQ or is that completely wrong?
Thanks :)
2026-04-04 01:00:25.1775264425
What's the Disjunctive normal form of a tautology
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Yes; the DNF can be built-up from the truth-table of the formula.
Let the formula $E$ has $p+q$ lines in his truth table with $p$ evaluated to t and $q$ to f.
The formula is equivalent to a formula $D$ of the form $D_1 \lor \ldots \lor D_p$ where $D_1, \ldots D_p$ correspond to the respective lines with t.
Every $D_i$ is the conjunct of the literals : positive, if in that line it has value t and negative otherwise.
Thus, a tautology being identically true, we have a disjunct for every line in the table.