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Describe geometrically the following sets on the real line: \[\begin{array}{ll}{\text { (i) }\{x | x<0\} ;} & {\text { (ii) }\{x| | x |<1\}}; \\ {\text { (iii) }\{x| | x-a |<\varepsilon\} ;} & {\text { (iv) }\{x | a<x \leq b\}}; \\ {\text { (v) }\{x| | x |<0\}}. \end{array} \]
- Relations. Mappings
For example, all sets listed in Problem 7 of §§1–3 are...
- Relations. Mappings
20 maj 2022 · Exercise \(\PageIndex{7}\): Set operations. Let \(A = \{ r,e,a,s,o,n,i,g\}, B = \{m,a,t,h,e,t,i,c,l\} \) and \( C \) = the set of vowels. Calculate: \(A \cup B \cup C.\) \(A \cap B.\) \({C}^c\).
The set of all subsets of a set A is called the power set of A and denoted as ℘(A) or sometimes as 2A. For example, if A = {a,b}, ℘(A) = {∅, {a}, {b}, {a,b}}. From the example above: a ∈ A; {a} ⊆ A; {a} ∈ ℘(A) ∅ ⊆ A; ∅ ∉ A; ∅ ∈ ℘(A); ∅ ⊆ ℘(A) 1.6. Operations on sets: union, intersection.
Three important binary set operations are the union (U), intersection (∩), and cross product (x). A binary operation is called commutative if the order of the things it operates on doesn’t matter.
2.2 Set Operations: Introduction: Two, or more, sets can be combined in many different ways. For instance, starting with the set of Computer Science majors at your school and the set of Business majors at your school, we can form the set of students who are Computer Science majors or Business
we will prove theorems shedding light on this issue. Because the fundamentals of Set Theory are known to all mathemati-cians, basic problems in the subject seem elementary. Here are three simple statements about sets and functions. They look like they could appear on a homework assignment in an undergraduate course. 1.
If \(a\) is an element of set \(A\), we write \(a \in A\). If \(a\) is not an element of a set \(A\), we write \(a \notin A\). To specify a set, we can list all of its elements, if possible, or we can use a defining rule. For instance, to specify the fact that a set \(A\) contains four elements \(a, b, c, d\), we write \[A=\{a, b, c, d\}.\]
