Eyler-Venna Figures

Содержание и основные понятия

By table of contents
Chapter 29 Page 29.1
Eyler-Venna Figures
Logic Search · AND · OR · NOT · EGE No. 6
How to find math sites in Russian, but not in physics? With the help of the AND, OR, NOT diagrams, this is how EGE No. 6 works.
GEF
PIF
EEG No. 6
OGE No. 6
Where'd that come from?
In chapter 15, "Mathematical logic", we studied positional operations, and now we apply them geometrically: every many — circle, operation — a way to select the area in the diagram.
01
What's an Eulerian-Venna diagram?
Ideas
Each set is represented as a circle (or a closed area). Elements belonging to several sets are located in the intersection of circles.
For an online search, every "circle" is a request. The page falls into a circle if it contains this key word.
Three operations
Request
Zone
Meaning
A AND B
A ∩ B
Both words
A OR B
A ∪ B
Just one.
A AND NOT B
A \ B
A, but not B
⭕
Visualizer: diagram with 2 circles
A
B
A∩B
University U
Area selected: A AND B (intersection)
02
EGE Task #6: Logical Search
Task format
A table of Internet queries (number of pages) has been provided. The number of pages for a new request needs to be found using the data from the table.
Key to the solution:
draw a graph of Euler.
and express the areas through the data.
Typical EEG No. 6 format:
3 requests (A, B, C) are given a table with 4 to 7 numbers. Find the value of the combined request.
🔍
Eulerian diagram: 3 requests
a
b
c
ab
ac
bc
abc
A
B
C
Request A
Request B
Request C
Intersections
7 zones: a (A only), b (B only), c (C only), ab, ac, bc, abc (all three)
Key formulas (3 sets)
|A| = a + ab + ac + abc
|B| = b + ab + bc + abc
|C| = c + ac + bc + abc
|A AND B| = ab + abc
|A AND C| = ac + abc
|A OR B| = a + b + ab + ac + bc + abc = |A| + |B| - |A AND B|
|A AND B AND C| = abc
03
Interactive Coacher EGE No. 6
🎲
Task generator EGE No. 6 (logistical search)
Press "New Task" -- there will be a task in EGE No.6 format, decide, then check the answer.
04
EGE Decision No. 6 algorithm
📋
Footstep method
Draw a graph of Euler.
with the number of laps required (2 or 3).
Identify the variable areas:
a, b, c, ab, ac, bc, abc.
Draw a system of equations
from the data of the table (each row = one equation).
Set the system.
- find the value of all the zones.
Compute the answer
- set up the right areas.
Case study
Condition:
The results of the requests (thousands of pages) are presented in the table:
Request
Pages (thousands)
Computer science
4000
Mathematics
5000
AND Mathematics
1500
Find:
AND NOT Information Technology
Обозначим: a = только Информатика, b = только Математика, ab = оба
a + ab = 4000 (запрос «Информатика»)
b + ab = 5000 (запрос «Математика»)
ab = 1500 (запрос «Информатика AND Математика»)
→ a = 4000 - 1500 = 2500
Ответ:
2500 тыс. страниц
🧮
Interactive calculator: ask your data
Enter the data for the two requests and cross-check them -- get all the areas of the chart.
A (thousands)
♪ B ♪ Request B (thousands)
*A AND B * — crossing (thousands)
Введи данные и нажми «Вычислить».
🎯
Mini-test: 5 questions on the theme
XP: 0 / 100
🧩
Check yourself out of the Eyler diagrams.
5 questions · 20 XP for each correct