Boolean Algebra Laws

Boolean algebra is named after the mathematician George Boole (1813-1864) and plays an important role in probabilistic safety analysis. Some of its law s are as follows [10-12]  

Boolean algebra is used to a degree in safety and reliability studies concerning oil and gas industry. Some of its laws that are considered useful to understand subsequent chapters of this book are presented below [3-6]  

) denotes the intersection of sets. Sometimes Equation 2.1 is written without the dot (e.g., AB), but it still conveys the same meaning. 

Boolean algebra plays an important role in various types of transportation system reliability and safety studies and is named after George Boole (1813-1864), a mathematician. Some of fhe Boolean algebra laws are as follows [3,4]  

X is an arbitrary set or event, y is an arbitrary set or event. + denotes the union of sets. 

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The algebra of sets-BooIean algebra-governs tlie way in wliich sets can be manipulated to form equivalent sets. The principal Boolean algebra laws used for tliis purpose are as follows. 

The book is composed of 11 chapters. Chapter 1 presents the various introductory aspects of patient safety including patient safety-related facts and figures, terms and definitions, and sources for obtaining useful information on patient safety. Chapter 2 reviews mathematical concepts considered useful to understand subsequent chapters and covers topics such as mode, median, mean deviation. Boolean algebra laws, probability definition and properties, Laplace transforms, and probability distributions. 

If the letter symbols for sets are replaced by numbers, tlie commutative and associative laws become familiar laws of aritlimetic. In Boolean algebra tlie first of tlie two distributive laws, Eq. (19.3.5), lias an analogous counterpart in arithmetic. Tlie second, Eq. (19.3.6), does not. In risk analysis. Boolean algebra is used to simplify e. pressions for complicated events. For example, consider tlie event... 

Applying tlie Boolean algebra associative law and distributive law, given in Eqs. 

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