36
Venn diagrams
Textbook: Part 1, lesson 36, pp. 111–113
GoalVenn diagrams: finding the intersection and union of sets.
New words
Venn diagram · Venn diagrammasiintersection · kesishmaunion · birlashmacommon element · umumiy element
Explanation
In a Venn diagram each set is drawn as a circle. The overlap of two circles is the intersection – elements that belong to both sets. The two circles together make the union – elements in at least one set. The number in the union = number in A + number in B − number in the intersection, because common elements are counted twice.
Worked examples
A = {2, 4, 6, 8, 10, 12}, B = {3, 6, 9, 12}. The intersection is {6, 12}. The union has 6 + 4 − 2 = 8 elements.
Of 30 pupils, 18 go to chess, 15 to art, 6 to both. Chess only: 18 − 6 = 12; at least one club: 18 + 15 − 6 = 27.
Class activity
“Two circles”: two hoops are laid on the floor; children stand in them according to properties (for example wears glasses, wears a watch) and those in the overlap are counted.
Practice
1
A = {1, 2, 3, 4, 5, 6} and B = {4, 5, 6, 7, 8}. Write their intersection.
{4, 5, 6}
2
Set A has 12 elements, set B has 9 and 5 are common. How many elements are in the union?
16
3
Of 28 pupils, 17 like football, 14 like swimming and 6 like both. How many like only football?
11
4
How many pupils in that class like neither sport?
3