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% Document Info
\author{bladabuska}
\pdfinfo{
  /Title (boolean-algebra.pdf)
  /Creator (Cheatography)
  /Author (bladabuska)
  /Subject (Boolean Algebra Cheat Sheet)
}

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    \vspace{-2pt}\large{\bf{\textcolor{DarkBackground}{\textrm{Boolean Algebra Cheat Sheet}}}} \\
    \normalsize{by \textcolor{DarkBackground}{bladabuska} via \textcolor{DarkBackground}{\uline{cheatography.com/173176/cs/46007/}}}
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  \mymulticolumn{2}{p{5.377cm}}{\bf\textcolor{white}{Cheatographer}}  \\
  \vspace{-2pt}bladabuska \\
  \uline{cheatography.com/bladabuska} \\
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  \mymulticolumn{1}{p{5.377cm}}{\bf\textcolor{white}{Cheat Sheet}}  \\
   \vspace{-2pt}Not Yet Published.\\
   Updated 25th March, 2025.\\
   Page {\thepage} of \pageref{LastPage}.
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  Measure your website readability!\\
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\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Introduction}}  \tn
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\mymulticolumn{1}{x{5.377cm}}{The Boolean algebra, named after the mathematician George Boole, is a branch of mathematics that deals with binary variables and logical operations. Developed in the mid-19th century, Boolean algebra laid the foundation for digital logic and computer science. It was primarily introduced as a way to express logical statements in a symbolic form, offering a method to manipulate logical propositions algebraically. \newline % Row Count 9 (+ 9)
The main idea behind Boolean algebra is to operate on binary values, typically represented as 0 (false) and 1 (true). The algebraic structure follows a set of basic operations: AND, OR, and NOT, which correspond to logical conjunction, disjunction, and negation. These operations are the backbone of digital circuits, making Boolean algebra crucial in the design of electronic systems such as computers, telecommunication devices, and automation systems. \newline % Row Count 19 (+ 10)
Boolean algebra has found extensive applications in various fields, most notably in the development of computer hardware and software. It is used to optimize circuits, simplify complex logical expressions, and create algorithms for decision-making processes. Over time, its influence has expanded, and it continues to be a vital component of modern computational technologies.% Row Count 27 (+ 8)
} \tn 
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\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Historic}}  \tn
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1847 & {\bf{George Boole}} published a pamphlet titled {\emph{The Mathematical Analysis of Logic}} in response to a controversy between {\bf{De Morgan}} and {\bf{Sir Hamilton}}. \tn 
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% Row 1
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1854 & {\bf{Boole}} published the book {\emph{The Laws of Thought}} with a different formulation from his previous work. \tn 
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1860s & Boolean algebra emerged in the works of {\bf{William Jevons}} and {\bf{Charles Peirce}}. \tn 
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1890 & {\bf{Schr{\"o}der}} published his best work, in three volumes, called {\emph{Vorlesungen über die Algebra der Logik}}. This work was the first systematic presentation of Boolean algebra and distributive matrices. \tn 
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1904 & The Boolean algebra is seen as an axiomatic algebraic structure thanks to the works of {\bf{Huntington}}. \tn 
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1927 & {\bf{Zhegalkin}} demonstrated that traditional algebra using integer numerical values modulo 2 (instead of the traditional modulo 10) behaves exactly like Boolean algebra. This fact has led to some ambiguity about the true nature of Boolean algebra: it can be understood as {\emph{logical algebra}} or as {\emph{numerical algebra}}. \tn 
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1930s & Boolean algebra became mathematically rigorous thanks to the works of {\bf{Marshall Stone}} (1930s), and to {\bf{Birkhoff's}} matrix theory (1940). \tn 
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1938 & {\bf{Shannon}} demonstrated that electronic circuits with relays could be modeled through Boolean algebra. \tn 
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\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{The Basics}}  \tn
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\mymulticolumn{1}{x{5.377cm}}{Boolean Algebra consists of a set of {\bf{values}}, {\bf{operations}}, and {\bf{axioms}}, from which {\bf{identities}} and {\bf{theorems}} are derived.% Row Count 3 (+ 3)
} \tn 
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\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Venn Diagrams}}  \tn
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\mymulticolumn{1}{x{5.377cm}}{{\bf{John Venn}} was a British mathematician and logician known for introducing {\bf{Venn diagrams}}, which visually represent relationships between sets. These diagrams simplify the understanding of operations like union, intersection, and complement, making them valuable in logic, statistics, and computer science. In {\bf{Boolean Algebra}}, they help visualize logical operations, aiding in the analysis of Boolean expressions, circuit simplification, and understanding fundamental principles of mathematical logic.% Row Count 11 (+ 11)
} \tn 
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% That's all folks
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