From d8434b9bb461ad950f303ca07f47838ca5673a38 Mon Sep 17 00:00:00 2001
From: Michael Leuschel <leuschel@uni-duesseldorf.de>
Date: Mon, 20 Apr 2020 17:20:15 +0200
Subject: [PATCH] fix typos
---
info4/kapitel-0/Logik.ipynb | 411 +++++++++++++++++++++++++++++-------
1 file changed, 337 insertions(+), 74 deletions(-)
diff --git a/info4/kapitel-0/Logik.ipynb b/info4/kapitel-0/Logik.ipynb
index 705e863..db02662 100644
--- a/info4/kapitel-0/Logik.ipynb
+++ b/info4/kapitel-0/Logik.ipynb
@@ -28,7 +28,6 @@
"* Code kann interaktiv ausgeführt werden\n",
"* Ergebnisse erscheinen im Notebook unter dem jeweiligem Code\n",
"* Ähnlich wie eine REPL (read-eval-print-loop), mit einigen Unterschieden:\n",
- " * Code-Abschnitte können \"außer der Reihe\" bearbeitet und ausgeführt werden\n",
" * Ausgaben können formatierten Text und Grafiken enthalten\n",
" * Speicherbar als Datei\n",
" * Code kann später neu ausgeführt werden\n",
@@ -46,12 +45,8 @@
"* Open Source und plattformübergreifend\n",
"* Stammt aus der Python-Community, in Python implementiert\n",
"* ACM System Software Award 2017\n",
- "* Jupyter-Notebooks können aber verschiedene Programmiersprachen verwenden\n",
- "* Dazu trennt Jupyter strikt zwischen Frontend und Kernel:\n",
- " * Das allgemeine **Frontend** implementiert z. B. Benutzeroberfläche und Dateiformat\n",
- " * Ein sprachspezifischer **Kernel** stellt die Sprache dem Frontend zur Verfügung\n",
- "* Schnittstellen zwischen Frontend und Kernel sind sprachneutral\n",
- " * Kernel können in (fast) jeder Sprache implementiert werden, kein Python-Code nötig\n",
+ "* Jupyter-Notebooks verschiedene Programmiersprachen verwenden\n",
+ " * Ein sprachspezifischer **Kernel** stellt die Sprache dem Jupyter Frontend zur Verfügung\n",
" "
]
},
@@ -149,7 +144,7 @@
},
{
"cell_type": "code",
- "execution_count": 30,
+ "execution_count": 1,
"metadata": {},
"outputs": [
{
@@ -161,7 +156,7 @@
"TRUE"
]
},
- "execution_count": 30,
+ "execution_count": 1,
"metadata": {},
"output_type": "execute_result"
}
@@ -172,7 +167,7 @@
},
{
"cell_type": "code",
- "execution_count": 31,
+ "execution_count": 2,
"metadata": {},
"outputs": [
{
@@ -184,7 +179,7 @@
"TRUE"
]
},
- "execution_count": 31,
+ "execution_count": 2,
"metadata": {},
"output_type": "execute_result"
}
@@ -195,7 +190,7 @@
},
{
"cell_type": "code",
- "execution_count": 32,
+ "execution_count": 3,
"metadata": {},
"outputs": [
{
@@ -207,7 +202,7 @@
"FALSE"
]
},
- "execution_count": 32,
+ "execution_count": 3,
"metadata": {},
"output_type": "execute_result"
}
@@ -230,7 +225,7 @@
},
{
"cell_type": "code",
- "execution_count": 33,
+ "execution_count": 4,
"metadata": {},
"outputs": [
{
@@ -242,7 +237,7 @@
"TRUE"
]
},
- "execution_count": 33,
+ "execution_count": 4,
"metadata": {},
"output_type": "execute_result"
}
@@ -251,6 +246,29 @@
"¬(2<1)"
]
},
+ {
+ "cell_type": "code",
+ "execution_count": 6,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/markdown": [
+ "$\\mathit{FALSE}$"
+ ],
+ "text/plain": [
+ "FALSE"
+ ]
+ },
+ "execution_count": 6,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "¬(1+1=2)"
+ ]
+ },
{
"cell_type": "markdown",
"metadata": {},
@@ -267,7 +285,7 @@
},
{
"cell_type": "code",
- "execution_count": 34,
+ "execution_count": 7,
"metadata": {},
"outputs": [
{
@@ -279,7 +297,7 @@
"TRUE"
]
},
- "execution_count": 34,
+ "execution_count": 7,
"metadata": {},
"output_type": "execute_result"
}
@@ -290,7 +308,7 @@
},
{
"cell_type": "code",
- "execution_count": 35,
+ "execution_count": 8,
"metadata": {},
"outputs": [
{
@@ -302,7 +320,7 @@
"FALSE"
]
},
- "execution_count": 35,
+ "execution_count": 8,
"metadata": {},
"output_type": "execute_result"
}
@@ -320,30 +338,30 @@
},
{
"cell_type": "code",
- "execution_count": 36,
+ "execution_count": 11,
"metadata": {},
"outputs": [
{
"data": {
"text/markdown": [
- "$\\mathit{TRUE}$"
+ "$\\mathit{FALSE}$"
],
"text/plain": [
- "TRUE"
+ "FALSE"
]
},
- "execution_count": 36,
+ "execution_count": 11,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
- "2>1 ∨ 1>2"
+ "1>1 ∨ 1>2"
]
},
{
"cell_type": "code",
- "execution_count": 37,
+ "execution_count": 10,
"metadata": {},
"outputs": [
{
@@ -355,7 +373,7 @@
"TRUE"
]
},
- "execution_count": 37,
+ "execution_count": 10,
"metadata": {},
"output_type": "execute_result"
}
@@ -373,7 +391,7 @@
},
{
"cell_type": "code",
- "execution_count": 38,
+ "execution_count": 12,
"metadata": {},
"outputs": [
{
@@ -385,7 +403,7 @@
"TRUE"
]
},
- "execution_count": 38,
+ "execution_count": 12,
"metadata": {},
"output_type": "execute_result"
}
@@ -396,7 +414,7 @@
},
{
"cell_type": "code",
- "execution_count": 39,
+ "execution_count": 13,
"metadata": {},
"outputs": [
{
@@ -408,7 +426,7 @@
"TRUE"
]
},
- "execution_count": 39,
+ "execution_count": 13,
"metadata": {},
"output_type": "execute_result"
}
@@ -419,7 +437,7 @@
},
{
"cell_type": "code",
- "execution_count": 40,
+ "execution_count": 14,
"metadata": {},
"outputs": [
{
@@ -431,7 +449,7 @@
"FALSE"
]
},
- "execution_count": 40,
+ "execution_count": 14,
"metadata": {},
"output_type": "execute_result"
}
@@ -449,7 +467,7 @@
},
{
"cell_type": "code",
- "execution_count": 41,
+ "execution_count": 15,
"metadata": {},
"outputs": [
{
@@ -461,7 +479,7 @@
"TRUE"
]
},
- "execution_count": 41,
+ "execution_count": 15,
"metadata": {},
"output_type": "execute_result"
}
@@ -472,7 +490,7 @@
},
{
"cell_type": "code",
- "execution_count": 42,
+ "execution_count": 16,
"metadata": {},
"outputs": [
{
@@ -484,7 +502,7 @@
"TRUE"
]
},
- "execution_count": 42,
+ "execution_count": 16,
"metadata": {},
"output_type": "execute_result"
}
@@ -495,7 +513,7 @@
},
{
"cell_type": "code",
- "execution_count": 43,
+ "execution_count": 17,
"metadata": {},
"outputs": [
{
@@ -507,7 +525,7 @@
"FALSE"
]
},
- "execution_count": 43,
+ "execution_count": 17,
"metadata": {},
"output_type": "execute_result"
}
@@ -524,14 +542,14 @@
"\n",
"Anmerkung: Wir nehmen an, dass $\\neg$ am stärksten bindet, dann kommen $\\wedge$, $\\vee$, $\\Rightarrow$ und schließlich ⇔.\n",
"\n",
- "Die Formel $(p \\vee (\\neg p \\wedge q)$ steht also für $(p \\vee (\\neg(p) \\wedge q)$.\n",
+ "Die Formel $(p \\vee (\\neg p \\wedge q))$ steht also für $(p \\vee (\\neg(p) \\wedge q)$.\n",
"\n",
"Eine Formel kann man immer als einen Baum sehen"
]
},
{
"cell_type": "code",
- "execution_count": 44,
+ "execution_count": 18,
"metadata": {},
"outputs": [
{
@@ -540,7 +558,7 @@
"Preference changed: OPTIMIZE_AST = FALSE\n"
]
},
- "execution_count": 44,
+ "execution_count": 18,
"metadata": {},
"output_type": "execute_result"
}
@@ -551,7 +569,7 @@
},
{
"cell_type": "code",
- "execution_count": 45,
+ "execution_count": 19,
"metadata": {},
"outputs": [
{
@@ -773,7 +791,7 @@
"<Dot visualization: formula_tree [(2>3 => 4>1) <=> not(5<1)]>"
]
},
- "execution_count": 45,
+ "execution_count": 19,
"metadata": {},
"output_type": "execute_result"
}
@@ -792,7 +810,7 @@
"\n",
"<img src=\"./img/wahrheitstabelle.png\" width=\"600\">\n",
"\n",
- "Wie berechnet man damit den Wahrheitswert einer Formel wie $(p \\vee (\\neg p \\wedge q)$?\n",
+ "Wie berechnet man damit den Wahrheitswert einer Formel wie $(p \\vee (\\neg p \\wedge q))$?\n",
"\n",
"\n",
"\n"
@@ -816,8 +834,8 @@
"Sei $i$ = $\\{p\\mapsto TRUE,q\\mapsto FALSE\\}$ eine Interpretation für die Formel $(p \\vee (\\neg p \\wedge q)$.\n",
"\n",
"* Schritt 1: alle Aussagen berechnen: $(TRUE \\vee (\\neg TRUE \\wedge FALSE)$\n",
- "* Schritt 2: $\\neg TRUE = FALSE$: $(TRUE \\vee (FALSE \\wedge FALSE)$\n",
- "* Schritt 3: $FALSE \\wedge FALSE = FALSE$: $(TRUE \\vee FALSE)$\n",
+ "* Schritt 2: $\\neg TRUE = FALSE$: $(TRUE \\vee (FALSE \\wedge FALSE)$\n",
+ "* Schritt 3: $FALSE \\wedge FALSE = FALSE$: $(TRUE \\vee FALSE)$\n",
"* Schritt 3: $TRUE \\vee FALSE = TRUE$: $TRUE$\n",
"\n",
"Unter der Interpretation $i$ ist die Formel $(p \\vee (\\neg p \\wedge q)$ wahr."
@@ -854,13 +872,13 @@
"\n",
"Zwei Formeln sind <b>äquivalent</b> gdw sie die selben Modelle haben.\n",
"\n",
- "$(p \\vee (\\neg p \\wedge q)$ ist zum Beispiel äquivalent zu $p \\vee q$.\n",
+ "$(p \\vee (\\neg p \\wedge q))$ ist zum Beispiel äquivalent zu $p \\vee q$.\n",
"Hier stellen wir die Interpretationen und Modelle tabellarisch dar:"
]
},
{
"cell_type": "code",
- "execution_count": 47,
+ "execution_count": 20,
"metadata": {},
"outputs": [
{
@@ -881,7 +899,7 @@
"TRUE\tTRUE\tTRUE\tTRUE\n"
]
},
- "execution_count": 47,
+ "execution_count": 20,
"metadata": {},
"output_type": "execute_result"
}
@@ -897,7 +915,7 @@
"cell_type": "markdown",
"metadata": {},
"source": [
- "Wir schreiben diesen Tatbestand als $(p \\vee (\\neg p \\wedge q) \\equiv p \\vee q$.\n",
+ "Wir schreiben diesen Tatbestand als $(p \\vee (\\neg p \\wedge q)) \\equiv p \\vee q$.\n",
"\n",
"Kleine Anmerkung: das Werkzeug im Jupyter Notebook akzeptiert keine aussagenlogische Variablen sondern nur Bool'sche Datenvariablen. Anstatt $p$ muss man ```p=TRUE``` schreiben und anstatt $p \\vee q$ muss man ```p=TRUE ∨ q=TRUE``` schreiben. Mit ```bool(P)``` konvertiert man den Wahrheitswert einer Formel in einen Bool'schen Datenwert um.\n",
"\n",
@@ -928,9 +946,32 @@
},
{
"cell_type": "code",
- "execution_count": null,
+ "execution_count": 21,
"metadata": {},
- "outputs": [],
+ "outputs": [
+ {
+ "data": {
+ "text/markdown": [
+ "|p|q|ODER|NODER|NUND|np|nq|\n",
+ "|---|---|---|---|---|---|---|\n",
+ "|$\\mathit{FALSE}$|$\\mathit{FALSE}$|$\\mathit{FALSE}$|$\\mathit{TRUE}$|$\\mathit{TRUE}$|$\\mathit{TRUE}$|$\\mathit{TRUE}$|\n",
+ "|$\\mathit{FALSE}$|$\\mathit{TRUE}$|$\\mathit{TRUE}$|$\\mathit{FALSE}$|$\\mathit{FALSE}$|$\\mathit{TRUE}$|$\\mathit{FALSE}$|\n",
+ "|$\\mathit{TRUE}$|$\\mathit{FALSE}$|$\\mathit{TRUE}$|$\\mathit{FALSE}$|$\\mathit{FALSE}$|$\\mathit{FALSE}$|$\\mathit{TRUE}$|\n",
+ "|$\\mathit{TRUE}$|$\\mathit{TRUE}$|$\\mathit{TRUE}$|$\\mathit{FALSE}$|$\\mathit{FALSE}$|$\\mathit{FALSE}$|$\\mathit{FALSE}$|\n"
+ ],
+ "text/plain": [
+ "p\tq\tODER\tNODER\tNUND\tnp\tnq\n",
+ "FALSE\tFALSE\tFALSE\tTRUE\tTRUE\tTRUE\tTRUE\n",
+ "FALSE\tTRUE\tTRUE\tFALSE\tFALSE\tTRUE\tFALSE\n",
+ "TRUE\tFALSE\tTRUE\tFALSE\tFALSE\tFALSE\tTRUE\n",
+ "TRUE\tTRUE\tTRUE\tFALSE\tFALSE\tFALSE\tFALSE\n"
+ ]
+ },
+ "execution_count": 21,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
"source": [
":table {p,q,ODER,NODER,NUND,np,nq| p:BOOL & q:BOOL & np = bool(¬(p=TRUE)) & nq = bool(¬(q=TRUE)) &\n",
" ODER=bool(p=TRUE ∨ q=TRUE) &\n",
@@ -952,9 +993,32 @@
},
{
"cell_type": "code",
- "execution_count": null,
+ "execution_count": 22,
"metadata": {},
- "outputs": [],
+ "outputs": [
+ {
+ "data": {
+ "text/markdown": [
+ "|p|q|IMPL|KONT|np|nq|\n",
+ "|---|---|---|---|---|---|\n",
+ "|$\\mathit{FALSE}$|$\\mathit{FALSE}$|$\\mathit{TRUE}$|$\\mathit{TRUE}$|$\\mathit{TRUE}$|$\\mathit{TRUE}$|\n",
+ "|$\\mathit{FALSE}$|$\\mathit{TRUE}$|$\\mathit{TRUE}$|$\\mathit{TRUE}$|$\\mathit{TRUE}$|$\\mathit{FALSE}$|\n",
+ "|$\\mathit{TRUE}$|$\\mathit{FALSE}$|$\\mathit{FALSE}$|$\\mathit{FALSE}$|$\\mathit{FALSE}$|$\\mathit{TRUE}$|\n",
+ "|$\\mathit{TRUE}$|$\\mathit{TRUE}$|$\\mathit{TRUE}$|$\\mathit{TRUE}$|$\\mathit{FALSE}$|$\\mathit{FALSE}$|\n"
+ ],
+ "text/plain": [
+ "p\tq\tIMPL\tKONT\tnp\tnq\n",
+ "FALSE\tFALSE\tTRUE\tTRUE\tTRUE\tTRUE\n",
+ "FALSE\tTRUE\tTRUE\tTRUE\tTRUE\tFALSE\n",
+ "TRUE\tFALSE\tFALSE\tFALSE\tFALSE\tTRUE\n",
+ "TRUE\tTRUE\tTRUE\tTRUE\tFALSE\tFALSE\n"
+ ]
+ },
+ "execution_count": 22,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
"source": [
":table {p,q,IMPL,KONT,np,nq| p:BOOL & q:BOOL & np = bool(¬(p=TRUE)) & nq = bool(¬(q=TRUE)) &\n",
" IMPL=bool(p=TRUE => q=TRUE) &\n",
@@ -976,7 +1040,7 @@
"# Logisches Schließen\n",
"Wenn $p \\wedge q$ gilt, dann ist $p$ eine logische Konsequenz (Schlussfolgerung) von $p\\wedge q$.\n",
"* Wir schreiben dies als $p \\wedge q \\models p$\n",
- "* Formal bedeutet dies, dass alle Modelle von $q \\wedge p$ auch Modelle von $p$ sind.\n",
+ "* Formal bedeutet dies, dass alle Modelle von $p \\wedge q$ auch Modelle von $p$ sind.\n",
"\n",
"Die Tabelle zeigt, dass $p \\Leftrightarrow q \\models p \\Rightarrow q$.\n",
"Die beiden Formeln sind nicht äquivalent."
@@ -984,9 +1048,32 @@
},
{
"cell_type": "code",
- "execution_count": null,
+ "execution_count": 24,
"metadata": {},
- "outputs": [],
+ "outputs": [
+ {
+ "data": {
+ "text/markdown": [
+ "|p|q|F1|F2|\n",
+ "|---|---|---|---|\n",
+ "|$\\mathit{FALSE}$|$\\mathit{FALSE}$|$\\mathit{TRUE}$|$\\mathit{TRUE}$|\n",
+ "|$\\mathit{FALSE}$|$\\mathit{TRUE}$|$\\mathit{FALSE}$|$\\mathit{TRUE}$|\n",
+ "|$\\mathit{TRUE}$|$\\mathit{FALSE}$|$\\mathit{FALSE}$|$\\mathit{FALSE}$|\n",
+ "|$\\mathit{TRUE}$|$\\mathit{TRUE}$|$\\mathit{TRUE}$|$\\mathit{TRUE}$|\n"
+ ],
+ "text/plain": [
+ "p\tq\tF1\tF2\n",
+ "FALSE\tFALSE\tTRUE\tTRUE\n",
+ "FALSE\tTRUE\tFALSE\tTRUE\n",
+ "TRUE\tFALSE\tFALSE\tFALSE\n",
+ "TRUE\tTRUE\tTRUE\tTRUE\n"
+ ]
+ },
+ "execution_count": 24,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
"source": [
":table {p,q,F1,F2| p:BOOL & q:BOOL & F1=bool(p=TRUE ⇔ q=TRUE) & F2=bool(p=TRUE ⇒ q=TRUE)}"
]
@@ -1054,9 +1141,32 @@
},
{
"cell_type": "code",
- "execution_count": null,
+ "execution_count": 25,
"metadata": {},
- "outputs": [],
+ "outputs": [
+ {
+ "data": {
+ "text/markdown": [
+ "|x|y|S1|S2|Puzzle|\n",
+ "|---|---|---|---|---|\n",
+ "|$\\mathit{FALSE}$|$\\mathit{FALSE}$|$\\mathit{TRUE}$|$\\mathit{TRUE}$|$\\mathit{TRUE}$|\n",
+ "|$\\mathit{FALSE}$|$\\mathit{TRUE}$|$\\mathit{FALSE}$|$\\mathit{TRUE}$|$\\mathit{FALSE}$|\n",
+ "|$\\mathit{TRUE}$|$\\mathit{FALSE}$|$\\mathit{FALSE}$|$\\mathit{FALSE}$|$\\mathit{FALSE}$|\n",
+ "|$\\mathit{TRUE}$|$\\mathit{TRUE}$|$\\mathit{TRUE}$|$\\mathit{FALSE}$|$\\mathit{FALSE}$|\n"
+ ],
+ "text/plain": [
+ "x\ty\tS1\tS2\tPuzzle\n",
+ "FALSE\tFALSE\tTRUE\tTRUE\tTRUE\n",
+ "FALSE\tTRUE\tFALSE\tTRUE\tFALSE\n",
+ "TRUE\tFALSE\tFALSE\tFALSE\tFALSE\n",
+ "TRUE\tTRUE\tTRUE\tFALSE\tFALSE\n"
+ ]
+ },
+ "execution_count": 25,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
"source": [
":table {x,y,S1,S2,Puzzle | x:BOOL & y:BOOL & \n",
" S1=bool(x=TRUE ⇔ y=TRUE) &\n",
@@ -1081,9 +1191,32 @@
},
{
"cell_type": "code",
- "execution_count": null,
+ "execution_count": 27,
"metadata": {},
- "outputs": [],
+ "outputs": [
+ {
+ "data": {
+ "text/markdown": [
+ "|x|y|S1|S2|Puzzle|\n",
+ "|---|---|---|---|---|\n",
+ "|$\\mathit{FALSE}$|$\\mathit{FALSE}$|$\\mathit{TRUE}$|$\\mathit{TRUE}$|$\\mathit{TRUE}$|\n",
+ "|$\\mathit{FALSE}$|$\\mathit{TRUE}$|$\\mathit{TRUE}$|$\\mathit{TRUE}$|$\\mathit{TRUE}$|\n",
+ "|$\\mathit{TRUE}$|$\\mathit{FALSE}$|$\\mathit{FALSE}$|$\\mathit{TRUE}$|$\\mathit{FALSE}$|\n",
+ "|$\\mathit{TRUE}$|$\\mathit{TRUE}$|$\\mathit{TRUE}$|$\\mathit{FALSE}$|$\\mathit{FALSE}$|\n"
+ ],
+ "text/plain": [
+ "x\ty\tS1\tS2\tPuzzle\n",
+ "FALSE\tFALSE\tTRUE\tTRUE\tTRUE\n",
+ "FALSE\tTRUE\tTRUE\tTRUE\tTRUE\n",
+ "TRUE\tFALSE\tFALSE\tTRUE\tFALSE\n",
+ "TRUE\tTRUE\tTRUE\tFALSE\tFALSE\n"
+ ]
+ },
+ "execution_count": 27,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
"source": [
":table {x,y,S1,S2,Puzzle | x:BOOL & y:BOOL & \n",
" S1=bool(x=TRUE ⇒ y=TRUE) &\n",
@@ -1131,9 +1264,32 @@
},
{
"cell_type": "code",
- "execution_count": null,
+ "execution_count": 28,
"metadata": {},
- "outputs": [],
+ "outputs": [
+ {
+ "data": {
+ "text/markdown": [
+ "|x|y|S1|S2|Puzzle|WS|\n",
+ "|---|---|---|---|---|---|\n",
+ "|$\\mathit{FALSE}$|$\\mathit{FALSE}$|$\\mathit{TRUE}$|$\\mathit{TRUE}$|$\\mathit{TRUE}$|$\\mathit{FALSE}$|\n",
+ "|$\\mathit{FALSE}$|$\\mathit{TRUE}$|$\\mathit{FALSE}$|$\\mathit{TRUE}$|$\\mathit{FALSE}$|$\\mathit{FALSE}$|\n",
+ "|$\\mathit{TRUE}$|$\\mathit{FALSE}$|$\\mathit{FALSE}$|$\\mathit{FALSE}$|$\\mathit{FALSE}$|$\\mathit{FALSE}$|\n",
+ "|$\\mathit{TRUE}$|$\\mathit{TRUE}$|$\\mathit{TRUE}$|$\\mathit{FALSE}$|$\\mathit{FALSE}$|$\\mathit{FALSE}$|\n"
+ ],
+ "text/plain": [
+ "x\ty\tS1\tS2\tPuzzle\tWS\n",
+ "FALSE\tFALSE\tTRUE\tTRUE\tTRUE\tFALSE\n",
+ "FALSE\tTRUE\tFALSE\tTRUE\tFALSE\tFALSE\n",
+ "TRUE\tFALSE\tFALSE\tFALSE\tFALSE\tFALSE\n",
+ "TRUE\tTRUE\tTRUE\tFALSE\tFALSE\tFALSE\n"
+ ]
+ },
+ "execution_count": 28,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
"source": [
":table {x,y,S1,S2,Puzzle,WS | x:BOOL & y:BOOL & \n",
" S1=bool(x=TRUE ⇔ y=TRUE) &\n",
@@ -1195,7 +1351,7 @@
"wobei immer gilt $\\phi_1 \\wedge ...\\phi_i \\models \\phi_{i+1}$.\n",
" \n",
"Wir haben per Transitiviät von $\\models$, dass $\\phi_1 \\models \\phi_k$.\n",
- "Aber im Gegensatz zum Äquivalenzbeweis gilt hier generell nicht $\\phi_k \\models phi_1$!\n",
+ "Aber im Gegensatz zum Äquivalenzbeweis gilt hier generell nicht $\\phi_k \\models \\phi_1$!\n",
"Dieser Beweis kann nicht umgekehrt werden.\n",
"\n"
]
@@ -1267,9 +1423,36 @@
},
{
"cell_type": "code",
- "execution_count": null,
+ "execution_count": 29,
"metadata": {},
- "outputs": [],
+ "outputs": [
+ {
+ "data": {
+ "text/markdown": [
+ "|x|y|res|\n",
+ "|---|---|---|\n",
+ "|$1$|$1$|$\\mathit{FALSE}$|\n",
+ "|$1$|$2$|$\\mathit{TRUE}$|\n",
+ "|$1$|$3$|$\\mathit{TRUE}$|\n",
+ "|$2$|$1$|$\\mathit{FALSE}$|\n",
+ "|$2$|$2$|$\\mathit{FALSE}$|\n",
+ "|$2$|$3$|$\\mathit{TRUE}$|\n"
+ ],
+ "text/plain": [
+ "x\ty\tres\n",
+ "1\t1\tFALSE\n",
+ "1\t2\tTRUE\n",
+ "1\t3\tTRUE\n",
+ "2\t1\tFALSE\n",
+ "2\t2\tFALSE\n",
+ "2\t3\tTRUE\n"
+ ]
+ },
+ "execution_count": 29,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
"source": [
":table {x,y,res | x:1..2 & y:1..3 & res=bool(x<y)}"
]
@@ -1313,9 +1496,29 @@
},
{
"cell_type": "code",
- "execution_count": null,
+ "execution_count": 30,
"metadata": {},
- "outputs": [],
+ "outputs": [
+ {
+ "data": {
+ "text/markdown": [
+ "$\\mathit{TRUE}$\n",
+ "\n",
+ "**Solution:**\n",
+ "* $\\mathit{x} = 0$"
+ ],
+ "text/plain": [
+ "TRUE\n",
+ "\n",
+ "Solution:\n",
+ "\tx = 0"
+ ]
+ },
+ "execution_count": 30,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
"source": [
"∃x.(x<5)"
]
@@ -1329,27 +1532,87 @@
},
{
"cell_type": "code",
- "execution_count": null,
+ "execution_count": 31,
"metadata": {},
- "outputs": [],
+ "outputs": [
+ {
+ "data": {
+ "text/markdown": [
+ "$\\mathit{TRUE}$\n",
+ "\n",
+ "**Solution:**\n",
+ "* $\\mathit{x} = 0$"
+ ],
+ "text/plain": [
+ "TRUE\n",
+ "\n",
+ "Solution:\n",
+ "\tx = 0"
+ ]
+ },
+ "execution_count": 31,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
"source": [
"x<5"
]
},
{
"cell_type": "code",
- "execution_count": null,
+ "execution_count": 32,
"metadata": {},
- "outputs": [],
+ "outputs": [
+ {
+ "data": {
+ "text/markdown": [
+ "$\\mathit{TRUE}$\n",
+ "\n",
+ "**Solution:**\n",
+ "* $\\mathit{x} = 10$"
+ ],
+ "text/plain": [
+ "TRUE\n",
+ "\n",
+ "Solution:\n",
+ "\tx = 10"
+ ]
+ },
+ "execution_count": 32,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
"source": [
"x+20 = 30"
]
},
{
"cell_type": "code",
- "execution_count": null,
+ "execution_count": 35,
"metadata": {},
- "outputs": [],
+ "outputs": [
+ {
+ "data": {
+ "text/markdown": [
+ "$\\mathit{TRUE}$\n",
+ "\n",
+ "**Solution:**\n",
+ "* $\\mathit{x} = -100$"
+ ],
+ "text/plain": [
+ "TRUE\n",
+ "\n",
+ "Solution:\n",
+ "\tx = −100"
+ ]
+ },
+ "execution_count": 35,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
"source": [
"x*x = 10000"
]
--
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