upd

2025-12-11 09:11:21 +03:00
parent faeaa4902e
commit 0910c1dd3d
7 changed files with 4638 additions and 1478 deletions
--- a/logic/.obsidian/app.json
+++ b/logic/.obsidian/app.json
@@ -0,0 +1 @@
+{}
--- a/logic/.obsidian/appearance.json
+++ b/logic/.obsidian/appearance.json
@@ -0,0 +1 @@
+{}
--- a/logic/.obsidian/core-plugins.json
+++ b/logic/.obsidian/core-plugins.json
@@ -0,0 +1,33 @@
+{
+  "file-explorer": true,
+  "global-search": true,
+  "switcher": true,
+  "graph": true,
+  "backlink": true,
+  "canvas": true,
+  "outgoing-link": true,
+  "tag-pane": true,
+  "footnotes": false,
+  "properties": true,
+  "page-preview": true,
+  "daily-notes": true,
+  "templates": true,
+  "note-composer": true,
+  "command-palette": true,
+  "slash-command": false,
+  "editor-status": true,
+  "bookmarks": true,
+  "markdown-importer": false,
+  "zk-prefixer": false,
+  "random-note": false,
+  "outline": true,
+  "word-count": true,
+  "slides": false,
+  "audio-recorder": false,
+  "workspaces": false,
+  "file-recovery": true,
+  "publish": false,
+  "sync": true,
+  "bases": true,
+  "webviewer": false
+}
--- a/logic/.obsidian/workspace.json
+++ b/logic/.obsidian/workspace.json
@@ -0,0 +1,192 @@
+{
+  "main": {
+    "id": "edb1ebea8169bc3e",
+    "type": "split",
+    "children": [
+      {
+        "id": "724d0ad68d510d57",
+        "type": "tabs",
+        "children": [
+          {
+            "id": "fe1e81558756c09c",
+            "type": "leaf",
+            "state": {
+              "type": "pdf",
+              "state": {
+                "file": "notes.pdf"
+              },
+              "icon": "lucide-file-text",
+              "title": "notes"
+            }
+          }
+        ]
+      }
+    ],
+    "direction": "vertical"
+  },
+  "left": {
+    "id": "4768e79537592808",
+    "type": "split",
+    "children": [
+      {
+        "id": "259febbe7265eb85",
+        "type": "tabs",
+        "children": [
+          {
+            "id": "4250c63d8e6ee2c8",
+            "type": "leaf",
+            "state": {
+              "type": "file-explorer",
+              "state": {
+                "sortOrder": "alphabetical",
+                "autoReveal": false
+              },
+              "icon": "lucide-folder-closed",
+              "title": "Files"
+            }
+          },
+          {
+            "id": "c38c35baa9c86283",
+            "type": "leaf",
+            "state": {
+              "type": "search",
+              "state": {
+                "query": "",
+                "matchingCase": false,
+                "explainSearch": false,
+                "collapseAll": false,
+                "extraContext": false,
+                "sortOrder": "alphabetical"
+              },
+              "icon": "lucide-search",
+              "title": "Search"
+            }
+          },
+          {
+            "id": "a3b3f8582066ac3c",
+            "type": "leaf",
+            "state": {
+              "type": "bookmarks",
+              "state": {},
+              "icon": "lucide-bookmark",
+              "title": "Bookmarks"
+            }
+          }
+        ]
+      }
+    ],
+    "direction": "horizontal",
+    "width": 300,
+    "collapsed": true
+  },
+  "right": {
+    "id": "4fe371b26b7fbd49",
+    "type": "split",
+    "children": [
+      {
+        "id": "a27e629e16416754",
+        "type": "tabs",
+        "children": [
+          {
+            "id": "2ac4dce4aeb43cbe",
+            "type": "leaf",
+            "state": {
+              "type": "backlink",
+              "state": {
+                "file": "notes.pdf",
+                "collapseAll": false,
+                "extraContext": false,
+                "sortOrder": "alphabetical",
+                "showSearch": false,
+                "searchQuery": "",
+                "backlinkCollapsed": false,
+                "unlinkedCollapsed": true
+              },
+              "icon": "links-coming-in",
+              "title": "Backlinks for notes"
+            }
+          },
+          {
+            "id": "57570db4194fbe9d",
+            "type": "leaf",
+            "state": {
+              "type": "outgoing-link",
+              "state": {
+                "file": "notes.pdf",
+                "linksCollapsed": false,
+                "unlinkedCollapsed": true
+              },
+              "icon": "links-going-out",
+              "title": "Outgoing links from notes"
+            }
+          },
+          {
+            "id": "0736655696eeb3bb",
+            "type": "leaf",
+            "state": {
+              "type": "tag",
+              "state": {
+                "sortOrder": "frequency",
+                "useHierarchy": true,
+                "showSearch": false,
+                "searchQuery": ""
+              },
+              "icon": "lucide-tags",
+              "title": "Tags"
+            }
+          },
+          {
+            "id": "268a0417d71d91e3",
+            "type": "leaf",
+            "state": {
+              "type": "all-properties",
+              "state": {
+                "sortOrder": "frequency",
+                "showSearch": false,
+                "searchQuery": ""
+              },
+              "icon": "lucide-archive",
+              "title": "All properties"
+            }
+          },
+          {
+            "id": "12358fc23750235e",
+            "type": "leaf",
+            "state": {
+              "type": "outline",
+              "state": {
+                "file": "notes.pdf",
+                "followCursor": false,
+                "showSearch": false,
+                "searchQuery": ""
+              },
+              "icon": "lucide-list",
+              "title": "Outline of notes"
+            }
+          }
+        ]
+      }
+    ],
+    "direction": "horizontal",
+    "width": 300,
+    "collapsed": true
+  },
+  "left-ribbon": {
+    "hiddenItems": {
+      "switcher:Open quick switcher": false,
+      "graph:Open graph view": false,
+      "canvas:Create new canvas": false,
+      "daily-notes:Open today's daily note": false,
+      "templates:Insert template": false,
+      "command-palette:Open command palette": false,
+      "bases:Create new base": false
+    }
+  },
+  "active": "fe1e81558756c09c",
+  "lastOpenFiles": [
+    "notes.typ~",
+    "4.py~",
+    "4.py",
+    "notes.typ"
+  ]
+}
--- a/logic/4.py
+++ b/logic/4.py
@@ -0,0 +1,15 @@
+
+def f4(a, b):
+    return ((a <= b) and b) <= a
+
+
+def main():
+    print("a, b, f(a, b)")
+    for a in [0, 1]:
+        for b in [0, 1]:
+            print(a, b, int(f4(a, b)))
+
+
+        
+if __name__ == "__main__":
+    main()
--- a/logic/notes.pdf
+++ b/logic/notes.pdf
--- a/logic/notes.typ
+++ b/logic/notes.typ
@@ -0,0 +1,259 @@
+#set text(size: 1.5em, font: "Maple Mono")
+
+
+0. отрицание - $not$
+1. сильная дизъюнкция - $eq.triple.not " или " or.double$
+2. конъюнкция - $and$
+3. дизъюнкция - $or$
+4. эквивалентность - $eq.triple$
+5. импликация - $arrow " или " subset$
+
+$
+1 and 0 eq 0
+$
+
+#align(center)[
+  #figure(
+    table(columns: 3)[$a$][$b$][$a and b$][0][0][0][0][1][0][1][0][0][1][1][1],
+    supplement: [Табл.],
+    caption: [Таблица истинности для $and$.]
+  )
+]
+
+#align(center)[
+  #figure(
+    table(columns: 3)[$a$][$b$][$a or b$][0][0][0][0][1][1][1][0][1][1][1][1],
+    supplement: [Табл.],
+    caption: [Таблица истинности для $or$.]
+  )
+]
+
+#align(center)[
+  #figure(
+    table(columns: 3)[$a$][$b$][$a eq.triple b$][0][0][1][0][1][0][1][0][0][1][1][1],
+    supplement: [Табл.],
+    caption: [Таблица истинности для $eq.triple$.]
+  )
+]
+
+#align(center)[
+  #figure(
+    table(columns: 3)[$a$][$b$][$a arrow.double.not b$][0][0][0][0][1][1][1][0][1][1][1][0],
+    supplement: [Табл.],
+    caption: [Таблица истинности для $arrow.double.not$.]
+  )
+]
+
+#align(center)[
+  #figure(
+    table(columns: 3)[$a$][$b$][$a arrow b$][0][0][1][0][1][1][1][0][0][1][1][1],
+    supplement: [Табл.],
+    caption: [Таблица истинности для $arrow$.]
+  )
+]
+
+=== Задачи
+
+Пусть $a eq 1, b eq 0, c eq 1, d eq 0$
+
+$
+a and b eq 0 \ 
+a or b and c eq 1 \
+a eq.triple b eq 0 \
+a xor b eq 1 \
+a arrow b eq 0 \
+(a and b) or c eq 1 \
+a xor (b or c) eq 1 \
+(a arrow b) eq.triple c eq 0 \
+(a and c) arrow (b xor c) eq 1 \
+((a xor b) and (c arrow d)) or (a eq.triple d) eq 0 \
+a and b eq.triple c eq 0 \
+a or b xor c eq 1
+$
+
+=== Законы
+
+
+Закон двойного отрицания
+$
+not (not A) eq A \
+$
+
+Закон идемпотентности
+$
+A or A eq A \
+A and A eq A \
+$
+
+Закон коммутативности
+$
+A or B eq B or A \
+A and B eq B and A
+$
+
+Нейтральные элементы
+$
+A and 1 eq A \
+A or 0 eq A
+$
+
+Абсорбирующие элементы
+$
+A and 0 eq 0 \
+A or 1 eq 1
+$
+
+Законы отрицания
+$
+A and not A eq ? \
+A or not A eq ?
+$
+
+=== Еще примеры
+
+$
+A or (A and B) eq A
+
+/*
+A and (A or B)
+
+A or ¬A
+
+A and ¬A
+
+¬(¬A)
+
+(A or B) and A
+
+A or (B or A)
+
+(A and B) or B eq ?
+*/
+$
+
+Составить таблицы истинности для следующих функций:
+
+#align(center)[
+  #figure(
+    table(columns: 3)[$a$][$b$][$((a arrow b) and b) arrow a$][0][0][1][0][1][0][1][0][1][1][1][1],
+    supplement: [Табл.],
+    caption: [Таблица истинности для $((a arrow b) and b) arrow a$.]
+  )
+]
+
+#align(center)[
+  #figure(
+    table(columns: 2)[$a$][$A or (not A)$][0][1][1][1],
+    supplement: [Табл.],
+    caption: [Таблица истинности для $A or (not A)$.]
+  )
+]
+
+
+#align(center)[
+  #figure(
+    table(columns: 2)[$a$][$not (not A arrow.l.r A)$][0][0][1][0],
+    supplement: [Табл.],
+    caption: [Таблица истинности для $not (not A arrow.l.r A)$.]
+  )
+]
+
+#align(center)[
+  #figure(
+    table(columns: 2)[$p$][$p and (not p)$][0][0][1][0],
+    supplement: [Табл.],
+    caption: [Таблица истинности для $p and (not p)$.]
+  )
+]
+
+Задание 3.
+
+$
+C eq 0 \
+A or B or C eq A or B or 0 eq A or B eq 1 arrow.double A eq 1 " или " B eq 1 \
+A arrow (D or not D) eq A arrow 0 eq 1 arrow.double A eq 0 \
+B arrow (E and not E) eq B arrow 0 eq 1 arrow.double B eq 0 \
+A eq 1 " или " B eq 1, space.quad A eq 0 " и " B eq 0 arrow.double "противоречие" arrow.double C eq 1
+$
+
+
+
+
+=== Вариант 2
+
+Пусть $A$ - ложь (0), $B$ - истина (1).
+
+$
+A arrow B eq 1 
+B arrow A eq 0 
+not A arrow B eq 1  
+not B arrow A eq 1 
+not B arrow not A eq 1  
+not A arrow not B eq 0
+$
+
+Пусть $P eq 1, Q eq 0, R eq 0, S eq 1$:
+
+$
+R and S arrow (R arrow not Q or S) \
+0 and 1 arrow (0 arrow 1 or 1) \
+0 arrow (0 arrow 1) \
+0 arrow 1 \
+1
+$
+
+$
+P or R eq.triple R and not S \
+1 or 0 eq.triple 0 and not 1 \
+1 or 0 eq.triple 0 and 0 \
+1 eq.triple 0 \
+0
+$
+
+Составить таблицы истинности для следующих функций:
+
+#align(center)[
+  #figure(
+    table(columns: 2)[$P$][$(P arrow not P) and (not P arrow P)$][0][0][1][0],
+    supplement: [Табл.],
+    caption: [Таблица истинности для $(P arrow not P) and (not P arrow P)$.]
+  )
+]
+
+#align(center)[
+  #figure(
+    table(columns: 3)[$a$][$b$][$A and (A or B) eq.triple A $][0][0][1][0][1][1][1][0][1][1][1][1],
+    supplement: [Табл.],
+    caption: [Таблица истинности для $A and (A or B) eq.triple A $.]
+  )
+]
+
+
+
+
+
+#align(center)[
+  #figure(
+    table(columns: 2)[$p$][$p or (not p)$][0][1][1][1],
+    supplement: [Табл.],
+    caption: [Таблица истинности для $p or (not p)$.]
+  )
+]
+
+
+
+#align(center)[
+  #figure(
+    table(columns: 2)[$p$][$p and (not p)$][0][0][1][0],
+    supplement: [Табл.],
+    caption: [Таблица истинности для $p and (not p)$.]
+  )
+]
+
+Задание 3
+
+$
+not Q and R eq 1 arrow.double Q eq 0 \
+P arrow Q eq 1 arrow.double P arrow 0 eq 1 arrow.double P eq 0 \
+P eq 0
+$