131
Euler–Venn diagrams
Textbook: Part 4, lesson 131, pp. 66–68
GoalThe Euler–Venn diagram: showing a set inside an oval.
New words
diagram · diagrammaoval · ovalinside · ichidaoutside · tashqarisida
Explanation
To show a set we draw a closed line – an oval. We write the elements of the set inside the oval and numbers that do not belong to the set outside it. Such a drawing is called an Euler–Venn diagram, after two scientists, Leonhard Euler and John Venn. From the diagram we see at once whether an element belongs to the set or not.
Worked examples
B = {10, 20, 30, 40}. We write 10, 20, 30, 40 inside the oval. The number 35 is outside the oval: 35 ∉ B, while 30 ∈ B.
C is the set of weekend days. Inside the oval we may write “Saturday”, “Sunday” and outside it “Friday”, “Monday”.
Class activity
“A diagram made of people”: a loop of rope is laid out. Children make the set “wearing blue” by standing inside the loop while the others stay outside. Then the name of the set is changed.
Practice
1
A is the set of even natural numbers less than 10. Inside the oval are 2, 4, 6, 8 and outside are 3, 7, 10. How many elements are inside the oval?
4
2
Solve x + 30 = 75, y − 12 = 18, 5 × z = 100. Form the set M of the roots (in increasing order).
{20, 30, 45}
3
B is the set of natural numbers less than 20 that are multiples of 4. Which numbers do you write inside the oval?
{4, 8, 12, 16}
4
The oval shows numbers divisible by 2. Which of the numbers 14 and 15 is written outside the oval?
15