Problem 2.4 Let A and B be two sets with a finite number of elements. Show that the number of elements in AnB plus the number of elements in AU B is equal to the number of elements in A plus the number of elements in B. Problem 2.5 Show that if A and Bn (n= 1,2,3,.) are events, then An (UBn) = u (AN Bn) %3D 3D1 n=1
Problem 2.4 Let A and B be two sets with a finite number of elements. Show that the number of elements in AnB plus the number of elements in AU B is equal to the number of elements in A plus the number of elements in B. Problem 2.5 Show that if A and Bn (n= 1,2,3,.) are events, then An (UBn) = u (AN Bn) %3D 3D1 n=1
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![**Problem 2.4**
Let \( A \) and \( B \) be two sets with a finite number of elements. Show that the number of elements in \( A \cap B \) plus the number of elements in \( A \cup B \) is equal to the number of elements in \( A \) plus the number of elements in \( B \).
**Problem 2.5**
Show that if \( A \) and \( B_n \) \( (n = 1, 2, 3, \ldots) \) are events, then
\[
A \cap \left(\bigcup_{n=1}^{\infty} B_n\right) = \bigcup_{n=1}^{\infty} (A \cap B_n)
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F88290c14-c340-4cf2-9a35-bb9d74906999%2F0d7b26e6-9456-4d24-b57e-8658b2b69b09%2Fhyj1s7t_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem 2.4**
Let \( A \) and \( B \) be two sets with a finite number of elements. Show that the number of elements in \( A \cap B \) plus the number of elements in \( A \cup B \) is equal to the number of elements in \( A \) plus the number of elements in \( B \).
**Problem 2.5**
Show that if \( A \) and \( B_n \) \( (n = 1, 2, 3, \ldots) \) are events, then
\[
A \cap \left(\bigcup_{n=1}^{\infty} B_n\right) = \bigcup_{n=1}^{\infty} (A \cap B_n)
\]
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