| Disjunctive Normal Form |
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| CATEGORIES ABOUT DISJUNCTIVE NORMAL FORM | |
| boolean algebra | |
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: : : : However, the following formulas are not in DNF: : — NOT is the outermost operator : — an OR is nested within an AND Converting a formula to DNF involves using Logical Equivalence s, such as the Double Negative Law , De Morgan's Laws , and the Distributive Law . Note that all logical formulas can be converted into disjunctive normal form. However, in some cases conversion to DNF can lead to an exponential explosion of the formula. For example, in DNF form, logical formulas of the following form have 2n terms: : The following is a Formal Grammar for DNF: # <or> → ∨ # <and> → ∧ # <not> → ¬ # <disjunct> → <conjunct> # <disjunct> → <disjunct> <or> <conjunct> # <conjunct> → <literal> # <conjunct> → (<conjunct> <and> <literal>) # <literal> → <term> # <literal> → <not><term> Where <term> is any variable. SEE ALSO |
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