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<p>f(x, y, z) = (x ? y ? z ) ? ( ¬x ? y )</p> <p>g(x, y, z) = x ? ( y ? z )</p> <p>h(x, y, z) = (x ? y) ? (x ? y) ? z</p>

<p>Erzeugen Sie die disjunktive Normalform DNF(f) und die konjunktive Normalform KNF</p>

Solution
  • <table class="table table-condensed table-striped"> <tr> <th>x</th> <th>y</th> <th>z</th> <th>f1 ? x?y?z</th> <th>f2 ? ¬x?y</th> <th>f(x,y,z) f1?f2</th> <th>g(x,y,z) x?(y?z)</th> <th>f3 ? x?y</th> <th>h(x,y,z) f3?(x?y) ? z</th> </tr> <tr> <td>0</td> <td>0</td> <td>0</td> <td>0</td> <td>0</td> <td>0</td> <td>0</td> <td>0</td> <td>0</td> </tr> <tr> <td>0</td> <td>0</td> <td>1</td> <td>1</td> <td>0</td> <td>1</td> <td>0</td> <td>0</td> <td>1</td> </tr> <tr> <td>0</td> <td>1</td> <td>0</td> <td>0</td> <td>1</td> <td>1</td> <td>0</td> <td>1</td> <td>1</td> </tr> <tr> <td>0</td> <td>1</td> <td>1</td> <td>1</td> <td>1</td> <td>0</td> <td>0</td> <td>1</td> <td>1</td> </tr> <tr> <td>1</td> <td>0</td> <td>0</td> <td>0</td> <td>0</td> <td>0</td> <td>0</td> <td>1</td> <td>1</td> </tr> <tr> <td>1</td> <td>0</td> <td>1</td> <td>1</td> <td>0</td> <td>1</td> <td>1</td> <td>1</td> <td>1</td> </tr> <tr> <td>1</td> <td>1</td> <td>0</td> <td>1</td> <td>0</td> <td>1</td> <td>1</td> <td>0</td> <td>1</td> </tr> <tr> <td>1</td> <td>1</td> <td>1</td> <td>1</td> <td>0</td> <td>1</td> <td>1</td> <td>0</td> <td>1</td> </tr> </table>

    <h4>DNF</h4>

    <p>f (x, y, z) ``= (¬x ? ¬y ? z) ? (¬x ? y ? ¬z) ? (x ? ¬y ? z) ? (x ? y ? ¬z) ? (x ? y ? z) ``= (x ? y) ? (y ? ¬z) ? (¬y ? z)</p> <p>g (x, y, z) ``= (x ? ¬y ? z) ? (x ? y ? ¬z) ? (x ? y ? z) ``= (x?y)?(x?z)</p> <p>h (x, y, z) ``= (¬x ? ¬y ? z) ? (¬x ? y ? ¬z) ? (¬x ? y ? z) ? (x ? ¬y ? ¬z) ? ``(x ? ¬y ? z) ? (x ? y ? ¬z) ? (x ? y ? z) ``= x?y?z</p>

    <h4>KNF</h4>

    <p>f (x, y, z) ``= (x ? y ? z) ? (x ? ¬y ? ¬z) ? (¬x ? y ? z) ``= (x ? ¬y ? ¬z) ? (y ? z)</p> <p>g (x, y, z) ``= (x ? y ? z) ? (x ? y ? ¬z) ? (x ? ¬y ? z) ? (x ? ¬y ? ¬z) ? (¬x ? y ? z) ``= x ? (y ? z)</p> <p>h (x, y, z) ``= x ? y ? z</p>

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  • Subjects: computer-science
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  • Credits: 3
  • Difficulty: 0.5
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  • Note:
    HPI, Mathematik I - Diskrete Strukturen und Logik, Wintersemester 2012/2013
  • Created By: adius
  • Created At:
    2013-04-12 16:49:14 UTC
  • Last Modified:
    2013-04-12 16:49:14 UTC