Page 2: Intersection, Difference, and Complement of Sets
This page covers three more crucial działania na zbiorach: iloczyn zbiorów (intersection), różnica zbiorów (difference), and the complement of a set.
The iloczyn zbiorów is introduced first:
Definition: The intersection of sets A and B (A ∩ B) is the set of elements that belong simultaneously to both set A and set B.
Example: For A = {3,7,8} and B = {2,3,5,9}, the intersection A ∩ B = {3}.
Next, the page explains the różnica zbiorów:
Definition: The difference of sets A and B (A \ B) is the set of elements from A that do not belong to B.
Example: Given A = {3,7,8} and B = {2,3,5,9}, A \ B = {7,8} and B \ A = {2,5,9}.
The page also introduces the concept of the complement of a set:
Definition: The complement of set A with respect to the universal set U (A') is the set of elements in U that do not belong to A.
Highlight: Two important properties of set complements are: A' ∪ A = U and A' ∩ A = ∅.
Visual representations are used throughout to illustrate these działania na zbiorach, making it easier for students to understand these abstract concepts.
Vocabulary: "Iloczyn zbiorów" is Polish for intersection of sets, "różnica zbiorów" for set difference, and "dopełnienie zbioru" for complement of a set.
These operations are crucial for solving various działania na zbiorach zadania (set operation problems) in mathematics and are particularly important for students in działania na zbiorach klasa 1 liceum (set operations in 1st year of high school).
