How can I determine if a propositional formula is in DNF or CNF or both. What conditions must a propositional formula satisfy?
For example, why is $(a \land b)$ both in CNF and DNF?
How to determine if a propositional formula is in DNF or CNF or both
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logic
propositional-calculus
conjunctive-normal-form
disjunctive-normal-form
1 Answers
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It is $DNF$ because it can be seen as $$ ... \text{nothing} \vee (a \wedge b) \vee \text{nothing}... $$ And $CNF$ : $$ (...\text{nothing} \vee a \vee \text{nothing}...) \wedge (...\text{nothing} \vee b \vee \text{nothing}...) $$ By $nothing$ I don't mean something always true or false (even thought it can be thought of $\bot$) but simply there is nothing, no character.
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0For the `DNF`, does `...nothing`, `a` and `b` (and so on) represent conjunctive clauses? – 2017-01-04
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0The classical form of DNF is $(var_1\ \vee ... \vee\ var_n) \wedge\ ... \ (...)\ ...\ \wedge(var_\alpha\ \vee ... \vee\ var_\omega)$ so $a$ and $b$ represent boolean variables which can be of any number in any clauses. A clause may contain any number of variables separated by $\wedge$. So every "parenthesis-group" is a conjonctive clause. – 2017-01-04
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2You are switching the names. The first formula in your answer is in DNF and the second is in CNF. And instead of `nothing`, you could have used `false`. – 2017-01-04