Example of set thoery with probability question
Answers
Answer:
only for gi rls
Step-by-step explanation:
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Answer:
Probability theory uses the language of sets. As we will see later, probability is defined and calculated for sets. Thus, here we briefly review some basic concepts from set theory that are used in this book. We discuss set notations, definitions, and operations (such as intersections and unions). We then introduce countable and uncountable sets. Finally, we briefly discuss functions. This section may seem somewhat theoretical and thus less interesting than the rest of the book, but it lays the foundation for what is to come.
A set is a collection of some items (elements). We often use capital letters to denote a set. To define a set we can simply list all the elements in curly brackets, for example to define a set AA that consists of the two elements ♣♣ and ♢♢, we write A={♣,♢}A={♣,♢}. To say that ♢♢ belongs to AA, we write ♢∈A♢∈A, where "∈∈" is pronounced "belongs to." To say that an element does not belong to a set, we use ∉∉. For example, we may write ♡∉A♡∉A.
A set is a collection of things (elements).
Note that ordering does not matter, so the two sets {♣,♢}{♣,♢} and {♢,♣}{♢,♣} are equal. We often work with sets of numbers. Some important sets are given the following example.
Example
The following sets are used in this book:
The set of natural numbers, N={1,2,3,⋯}N={1,2,3,⋯}.
The set of integers, Z={⋯,−3,−2,−1,0,1,2,3,⋯}Z={⋯,−3,−2,−1,0,1,2,3,⋯}.
The set of rational numbers QQ.
The set of real numbers RR.
Closed intervals on the real line. For example, [2,3][2,3] is the set of all real numbers xx such that 2≤x≤32≤x≤3.
Open intervals on the real line. For example (−1,3)(−1,3) is the set of all real numbers xx such that −1<x<3−1<x<3.
Similarly, [1,2)[1,2) is the set of all real numbers xx such that 1≤x<21≤x<2.
The set of complex numbers CC is the set of numbers in the form of a+bia+bi, where a,b∈Ra,b∈R, and i=−1−−−