133
Intersection of sets
Textbook: Part 4, lesson 133, pp. 72–74
GoalIntersection of sets: A ∩ B, common elements; the empty intersection.
New words
intersection · kesishmacommon element · umumiy elementthe sign ∩ · belgi ∩empty set · bo‘sh to‘plam
Explanation
The set made of the common elements of A and B is called their intersection and is written A ∩ B. In a diagram two ovals partly overlap and the overlapping part shows the intersection. If there are no common elements, the intersection is the empty set: A ∩ B = ∅.
Worked examples
A = {5, 10, 15, 20, 25}, B = {10, 20, 30}. The numbers in both sets are 10 and 20. So A ∩ B = {10, 20}.
A = {1, 2, 3}, B = {4, 5}. There is no common element, so A ∩ B = ∅. With shapes: if A is red shapes and B is squares, then A ∩ B is red squares.
Class activity
“Two hoops”: two hoops are laid partly overlapping on the floor. One hoop is “wearing red”, the other “wearing a hat”. Children find their places; say who stands in the part that belongs to both hoops.
Practice
1
A = {1, 2, 3, 4, 5, 6}, B = {4, 5, 6, 7, 8}. Write A ∩ B.
{4, 5, 6}
2
A is the set of natural multiples of 4 up to 24 and B the set of natural multiples of 6 up to 24. Write A ∩ B.
{12, 24}
3
A = {a, b, c, d}, B = {c, d, e}. Write A ∩ B.
{c, d}
4
A is the set of even numbers and B the set of odd numbers. What is A ∩ B?
A ∩ B = ∅ (a number cannot be both even and odd).
5
A is the set of green shapes and B the set of circles. What shapes form A ∩ B?
Green circles