Problem 2.1 Suppose that a number z is to be selected from the real line R, and let A, B, and C be the events represented by the following subsets of R, where the notation {r: ---} denotes the set containing every point z for which the property presented following the colon is satisfied: A = {r:1
Problem 2.1 Suppose that a number z is to be selected from the real line R, and let A, B, and C be the events represented by the following subsets of R, where the notation {r: ---} denotes the set containing every point z for which the property presented following the colon is satisfied: A = {r: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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Transcribed Image Text:Problem 2.1
Suppose that a number r is to be selected from the real line R, and let A, B, and C be the
events represented by the following subsets of R, where the notation {r: ---} denotes the
set containing every point z for which the property presented following the colon is satisfied:
A = {r:1<x< 5}
B = {r:3<x<7}
C = {r:1<0}
Describe each of the following events as a set of real numbers:
(a) Aº
(b) AUB
(c) BnCe
(e) (AUB)nC
Problem 2.2
Toss a coin 4 times. Let A denote the event that a head is obtained on the first toss, and let
B denote the event that a head is obtained on the fourth toss. Is An B empty?
Problem 2.3
Let A and B be two sets.
(a) Show that (Aºn B®)° = AU B and (A° U B°)° = ANB.
(b) Consider rolling a six-sided die once. Let A be the set of outcomes where an odd number
comes up. Let B be the set of outcomes where a 1 or a 2 comes up. Calculate the sets
on both sides of the equalities in part (a), and verify that the equalities hold.
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 AUB 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= 1,2,3, ...) are events, then
An (U Bn) = U(An B„)
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