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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

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter1: Fundamental Concepts Of Algebra
Section1.2: Exponents And Radicals
Problem 90E
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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„)
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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