TU Wien:Diskrete Mathematik für Informatik VO (Gittenberger)/Schriftliche Prüfung 2014-02-04

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Task 1[Bearbeiten | Quelltext bearbeiten]

Find explicit expressions for and .

Task 2[Bearbeiten | Quelltext bearbeiten]

Let .

List all elements of

Prove or disprove that is a field.

Examine whether is a unit, and if so, calculate its inverse element.

Task 3[Bearbeiten | Quelltext bearbeiten]

Prove or disprove that the following functions are well-defined for all .

Task 4[Bearbeiten | Quelltext bearbeiten]

Calculate where is the Möbius function for the poset defined by this Hasse diagram:

   1
 / | \
|  |  c
a  b  |
|  |  d
 \ | /
   0