Page 1: Działania na przedziałach (Operations on Intervals)
This page introduces the concept of działania na przedziałach (operations on intervals) 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 (Numerical intervals): Continuous subsets of real numbers.
- Iloczyn przedziałów (Intersection of intervals): The set of all elements that belong to both intervals.
- Różnica przedziałów (Difference of intervals): 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 (square brackets) 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 (first year of high school).
