1 files changed, 144 insertions, 35 deletions

diff --git a/šola/ds1/kolokvij1.lyx b/šola/ds1/kolokvij1.lyx
index 01421eb..1df6ebc 100644
--- a/šola/ds1/kolokvij1.lyx
+++ b/šola/ds1/kolokvij1.lyx
@@ -68,7 +68,7 @@ enumitem
 \color #008000
 \end_index
 \leftmargin 1cm
-\topmargin 0cm
+\topmargin 1cm
 \rightmargin 1cm
 \bottommargin 2cm
 \headheight 1cm
@@ -94,33 +94,6 @@ enumitem
 
 \begin_body
 
-\begin_layout Title
-List s formulami za 1.
- kolokvij Diskretnih struktur 1
-\end_layout
-
-\begin_layout Author
-
-\noun on
-Anton Luka Šijanec
-\end_layout
-
-\begin_layout Date
-\begin_inset ERT
-status open
-
-\begin_layout Plain Layout
-
-
-\backslash
-today
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
 \begin_layout Standard
 \begin_inset ERT
 status open
@@ -353,7 +326,7 @@ Rightarrow C &
 \backslash
 vDash A
 \backslash
-Rightarrow B && 
+Rightarrow C && 
 \backslash
 text{
 \backslash
@@ -538,14 +511,100 @@ Množice
 \end_layout
 
 \begin_layout Standard
-\begin_inset Formula $^{\mathcal{C}},\cup\backslash,\cup\oplus$
+\begin_inset Formula $^{\mathcal{C}},\cap\backslash,\cup\oplus$
 \end_inset
 
  (left to right)
 \end_layout
 
 \begin_layout Standard
-\begin_inset Formula $\mathcal{A}\subseteq\mathcal{B}\Leftrightarrow\mathcal{A}\cup\mathcal{B}=\mathcal{B}\Leftrightarrow\mathcal{A}\cup\mathcal{B}=\mathcal{A}\Leftrightarrow\mathcal{A}\backslash\mathcal{B}=\left\{ \right\} \Leftrightarrow\mathcal{B}^{\mathcal{C}}\subseteq\mathcal{A^{\mathcal{C}}}$
+Distributivnost: 
+\begin_inset Formula $\cup\cap$
+\end_inset
+
+, 
+\begin_inset Formula $\cap\cup$
+\end_inset
+
+, 
+\begin_inset Formula $\left(\mathcal{A}\oplus\mathcal{B}\right)\cap\mathcal{C}=\left(\mathcal{A\cap\mathcal{C}}\right)\oplus\left(\mathcal{B}\cap\mathcal{C}\right)$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Asociativnost: 
+\begin_inset Formula $\oplus\cup\cap$
+\end_inset
+
+.
+ Distributivnost: 
+\begin_inset Formula $\oplus\cup\cap$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+Absorbcija: 
+\begin_inset Formula $\mathcal{A}\cup\left(\mathcal{A}\cap\mathcal{B}\right)=\mathcal{A}=A\cap\left(\mathcal{A}\cup\mathcal{B}\right)$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula $\mathcal{A}\subseteq\mathcal{B}\Leftrightarrow\mathcal{A}\cup\mathcal{B}=\mathcal{B}\Leftrightarrow\mathcal{A}\cup\mathcal{B}=\mathcal{A}\Leftrightarrow\mathcal{A}\backslash\mathcal{B}=\emptyset\Leftrightarrow\mathcal{B}^{\mathcal{C}}\subseteq\mathcal{A^{\mathcal{C}}}$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula $\mathcal{A}=\mathcal{B}\Longleftrightarrow\mathcal{A\oplus\mathcal{B}}=\emptyset$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula $\mathcal{A}=\emptyset\wedge\mathcal{B}=\emptyset\Longleftrightarrow\mathcal{A}\cup\mathcal{B}=\emptyset$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula $\left(\mathcal{X}\cap\mathcal{P}\right)\cup\left(\mathcal{X^{C}}\cap\mathcal{Q}\right)=\emptyset\Longleftrightarrow\text{\ensuremath{\mathcal{Q\subseteq X}\subseteq\mathcal{P^{C}}}}$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula $\mathcal{A}\backslash\mathcal{B}\sim\mathcal{A}\cap\mathcal{B}^{C}$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula $\mathcal{X}\cup\mathcal{X^{C}}=\emptyset$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula $\mathcal{W}=\mathcal{W}\cap\mathcal{U}=\mathcal{W\cap}\left(\mathcal{X}\cup\mathcal{X^{C}}\right)=\left(\mathcal{W}\cap\mathcal{X}\right)\cup\left(\mathcal{W}\cap\mathcal{X^{C}}\right)$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula $\mathcal{A}\oplus\mathcal{B}=\left(\mathcal{A}\backslash\mathcal{B}\right)\cup\left(\mathcal{B\backslash\mathcal{A}}\right)$
 \end_inset
 
 
@@ -557,6 +616,10 @@ Množice
 Lastnosti binarnih relacij
 \end_layout
 
+\begin_layout Standard
+
+\end_layout
+
 \begin_layout Paragraph
 \begin_inset ERT
 status open
@@ -1027,7 +1090,7 @@ Faktorska množica:
 \end_layout
 
 \begin_layout Standard
-\begin_inset Formula $\vec{\mathcal{B}}\text{ razbitje}A\Longleftrightarrow\bigcup_{i}\mathcal{B}_{i}=A\wedge\forall i\mathcal{B}_{i}\not=\left\{ \right\} \wedge\mathcal{B}_{i}\cap\mathcal{B}_{j}=\left\{ \right\} ,i\not=j$
+\begin_inset Formula $\vec{\mathcal{B}}\text{ razbitje}A\Longleftrightarrow\bigcup_{i}\mathcal{B}_{i}=A\wedge\forall i\mathcal{B}_{i}\not=\emptyset\wedge\mathcal{B}_{i}\cap\mathcal{B}_{j}=\emptyset,i\not=j$
 \end_inset
 
 
@@ -1109,12 +1172,58 @@ Srečno!
 \end_layout
 
 \begin_layout Paragraph
-TODO
+Funkcijska polnost
 \end_layout
 
 \begin_layout Standard
-Postovi teoremi za funkcijsko polnost, množice, preglej še zapiske s pisalnega
- stroja.
+\begin_inset Formula $T_{0},$
+\end_inset
+
+
+\begin_inset Formula $T_{1}$
+\end_inset
+
+, 
+\begin_inset Formula $S$
+\end_inset
+
+ – 
+\begin_inset Formula $f\left(\vec{x}\right)=\neg f\left(\vec{x}\oplus\vec{1}\right)$
+\end_inset
+
+, 
+\begin_inset Formula $L$
+\end_inset
+
+, 
+\begin_inset Formula $M$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula $L$
+\end_inset
+
+ – 
+\begin_inset Formula $f\left(\vec{x}\right)=\left[\begin{array}{ccc}
+a_{0} & \dots & a_{n}\end{array}\right]^{T}\oplus\wedge\left[\begin{array}{cccc}
+1 & x_{1} & \dots & x_{n}\end{array}\right]$
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula $M$
+\end_inset
+
+ – 
+\begin_inset Formula $\forall i,j:\vec{w_{i}}<\vec{w_{j}}\Rightarrow f\left(\vec{w_{i}}\right)\leq f\left(\vec{w_{j}}\right)$
+\end_inset
+
+
 \end_layout
 
 \begin_layout Standard