Propositional Logic: Logical consequence and consistency
Normal forms of logical formulas
Let \(p\) and \(q\) be propositional variables. Convert the logical formula \[p\rightarrow (q\land\neg\, q)\] into
Input hint: the formula editor does not (yet) recognise a symbol for the exclusive disjunction \(\oplus\), but it does accept the OpenMath input via \(\mathrm{Logic1.xor}\) with logical expressions separated by a comma. Use the given template.
- a disjunctive normal form (abbreviated DNF for Disjunctive Normal Form)
- the algebraic normal form (abbreviated ANF for Algebraic Normal Form).
Input hint: the formula editor does not (yet) recognise a symbol for the exclusive disjunction \(\oplus\), but it does accept the OpenMath input via \(\mathrm{Logic1.xor}\) with logical expressions separated by a comma. Use the given template.
| DNF of \(p\rightarrow (q\land\neg\, q)={}\) |
| ANF of \(p\rightarrow (q\land\neg\, q)={}\) |
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