Page 1: Działania na przedziałach (Operations on Intervals)
This page introduces the concept of działania na przedziałach operationsonintervals and provides examples and exercises to help students understand and practice these operations.
The lesson begins with an example demonstrating interval operations:
A = −4,7
B = −4,8
A ∩ B = 2,7
Definition: Interval operations include union U, intersection ∩, and difference − of sets represented as intervals on a number line.
The page then presents two main exercises:
Exercise 1.57:
a) A = −2,3 and B = 0,6
Solutions: A - B = −2,0, B - A = 3,6, A U B = −2,6, A ∩ B = 0,3
b) A = −∞,2 and B = 2,4
Solutions: A U B = −∞,4, A ∩ B = {2}
Example: For A = √3,∞ and B = −4,2, the union A U B = −4,∞ and the intersection A ∩ B = √3,2.
Exercise 1.58:
This exercise presents various interval pairs and asks students to perform different operations:
a) A = −5,1 and B = −2,4
b) A = 3,9 and B = 3,7
c) A = −∞,2 and B = √2,∞
d) A = −2,6 and B = 1,3
Highlight: The page includes a number line representation to visually aid students in understanding interval operations.
Vocabulary:
- Przedziały liczbowe Numericalintervals: Continuous subsets of real numbers.
- Iloczyn przedziałów Intersectionofintervals: The set of all elements that belong to both intervals.
- Różnica przedziałów Differenceofintervals: The set of elements that belong to one interval but not the other.
The page concludes with a reminder of interval notation, emphasizing the difference between open parentheses and closed squarebrackets intervals.
Quote: "U = przedział otwarty, [] = przedział zamknięty" ( = open interval, [] = closed interval)
This comprehensive lesson on działania na przedziałach zadania provides students with a solid foundation for understanding and performing operations on numerical intervals, an essential skill for advanced mathematical concepts in klasa 1 liceum firstyearofhighschool.
