From b0324289066876915efb84a133eca039d8e8c8ee Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Anton=20Luka=20=C5=A0ijanec?= Date: Sun, 17 Dec 2023 23:17:03 +0100 Subject: =?UTF-8?q?=C5=A1ola?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- "\305\241ola/ds1/kolokvij1.lyx" | 179 ++++++++++++++++++++++++++++++++-------- 1 file changed, 144 insertions(+), 35 deletions(-) (limited to 'šola/ds1') diff --git "a/\305\241ola/ds1/kolokvij1.lyx" "b/\305\241ola/ds1/kolokvij1.lyx" index 01421eb..1df6ebc 100644 --- "a/\305\241ola/ds1/kolokvij1.lyx" +++ "b/\305\241ola/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 -- cgit v1.2.3