China
Africa
Explore chapters and articles related to this topic
Exploring Mathematical Statements
Published in John D. Ross, Kendall C. Richards, Introductory Analysis, 2020
John D. Ross, Kendall C. Richards
If we know that we are primarily working inside of some “larger” set, we also have the notion of the complement of a set: Let A⊆ B. Then we define the complement of A in B, denoted B∖A, is the set of all elements of B that are not in A. If it is understood that we are working inside a known universal set U, we will sometimes denote the complement of A in U as simply Ac:=U∖A. Using this notation, it follows that if A and B are both subsets of the same universal set U, then B∖A=B∩Ac.Is it true that, given any two sets A and B, it follows that A∖B=B∖A?
Introduction to Fuzzy Sets: Basic Definitions and Relations
Published in Ali Zilouchian, Mo Jamshidi, Intelligent Control Systems Using Soft Computing Methodologies, 2001
Complement The complement of a set A, denoted A‾, is defined as the collection of all elements in the universe which do not reside in the set A (see Figure 8.4 ). The characteristic function μA‾ is defined by Equation 8.6 () ∀x∈U:μA‾=1-μA(x)
Introduction to Random Signals
Published in Shaila Dinkar Apte, Random Signal Processing, 2017
The complement of any set A is the set of all elements of the universal set, which are not included in set A. Let us first define the universal set. The universal set is defined as the set that consists of all elements for a particular situation or experiment. Let us consider the example of a rolling die. Here, for this experiment, there are only six possible elements or outcomes, namely, number 1 on the face, number 2 on the face, number 3 on the face, number 4 on the face, number 5 on the face, and number 6 on the face. We write this as the universal set S = {1, 2, 3, 4, 5, 6}. Let us define set A as A = {1, 2, 3}.
High-Dimensional Cost-constrained Regression Via Nonconvex Optimization
Published in Technometrics, 2022
We use the following notations throughout this article. The complement of a set S is denoted by Sc. For a vector V and a set S, we use VS to denote the subvector , and to denote the norm of the vector. For two vectors , we use to denote the inner product. For a matrix M and sets , we use to denote the submatrix of M with the row indices in the set S1 and the column indices in the set S2. For a symmetric matrix A, we use to denote the largest eigenvalue of the matrix. We use to denote the indicator function which equals to 1 if and 0 otherwise. The gradient of a function is denoted by . For a vector , we use to denote . Given an arbitrary set and a function , the arg min over the subset S is defined by .
Bi-Objective Optimization Method for Horizontal Fragmentation Problem in Relational Data Warehouses as a Linear Programming Problem
Published in Applied Artificial Intelligence, 2018
Mohamed Barr, Kamel Boukhalfa, Karima Bouibede
U is the universal set. The complement of the set A, denoted is the set of U elements that do not belong to A. In other words, the complement of the set A is the difference U-A (Niefield and Rosenthal 1985).