Database Design and Relational Theory
by C.J. Date · 19 Apr 2012 · 534pp · 118,459 words
in department D1 (which is not the default department number D3). Or a little more formally: NOT ( E5 is in D1 AND D1 ≠ D3 ) By De Morgan’s laws, this expression is equivalent to: E5 is not in D1 OR D1 = D3 Since D1 = D3 is false, this expression reduces to just “E5 is
RDF Database Systems: Triples Storage and SPARQL Query Processing
by Olivier Cure and Guillaume Blin · 10 Dec 2014
. Our first three axioms are already satisfying the form required by step 2 and the transformation of the last one results in ¬C ∧ ¬D, (using de Morgan's laws) which amounts to two new axioms with our representation: ¬C and ¬D. Our new axiom set is thus ¬A ∨ B ∨ C, A ∨ C ∨ D, ¬A
Eloquent JavaScript: A Modern Introduction to Programming
by Marijn Haverbeke · 15 Nov 2018 · 560pp · 135,629 words
finding such an element, we know that all elements matched and we should return true. To build every on top of some, we can apply De Morgan’s laws, which state that a && b equals !(!a || !b). This can be generalized to arrays, where all elements in the array match if there is no
The Art of Readable Code
by Dustin Boswell and Trevor Foucher · 14 Sep 2010
top tells the reader upfront that “this is a concept we’ll be referring to throughout this function.” Using De Morgan’s Laws If you ever took a course in circuits or logic, you might remember De Morgan’s laws. They are two ways to rewrite a boolean expression into an equivalent one: 1) not (a or b
The Logician and the Engineer: How George Boole and Claude Shannon Created the Information Age
by Paul J. Nahin · 27 Oct 2012 · 229pp · 67,599 words
to another English mathematician, Augustus De Morgan (Professor of Mathematics at University College, London), who formulated them in 1858.3 They are known today as De Morgan’s theorems. In the truth table I constructed to show that A + AB = A, the first two columns listed all possible values for the Boolean variables A
Concepts, Techniques, and Models of Computer Programming
by Peter Van-Roy and Seif Haridi · 15 Feb 2004 · 931pp · 79,142 words
representation. Propositional logic allows the expression of many simple laws. The contrapositive law (p → q) ↔ (¬q → ¬p) is a formula of propositional logic, as is De Morgan’s law ¬(p ∧ q) ↔ (¬p ∨ ¬q). To assign a truth-value to a propositional formula, we have to assign a truth-value to each of its atoms
Mapmatics: How We Navigate the World Through Numbers
by Paulina Rowinska · 5 Jun 2024 · 361pp · 100,834 words
US states at the same time, you need to head to the Four Corners Monument. * Students of logic will recognize De Morgan’s name from De Morgan’s laws, which describe the rules of negating logical statements. * In an ancient Greek myth, the Sphinx killed herself after Oedipus solved the riddle that she had
Erlang Programming
by Francesco Cesarini · 496pp · 70,263 words
to true if any expression evaluates to true. As an example of “... ; ...,...” notation, we can rewrite the guard function (after a couple of applications of De Morgan’s Laws) to the following: guard2(X,Y) when not(X>Y) , is_atom(X) ; not(is_atom(Y)) , X=/=3.4 -> X+Y. Simple combinations with
Code: The Hidden Language of Computer Hardware and Software
by Charles Petzold · 28 Sep 1999 · 566pp · 122,184 words
to a NAND gate: The output is 0 only if both inputs are 1. These two pairs of equivalent circuits represent an electrical implementation of De Morgan's Laws. Augustus De Morgan was another Victorianera mathematician, nine years older than Boole, whose book Formal Logic was published in 1847, the very same day (the
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of Boole's insights. He unselfishly encouraged Boole and helped him along the way, and is today sadly almost forgotten except for his famous laws. De Morgan's Laws are most simply expressed this way: A and B are two Boolean operands. In the first expression, they're inverted and then combined with the
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with the Boolean OR operator. This is the same as combining the operands with the Boolean AND operator and then inverting (which is the NAND). De Morgan's Laws are an important tool for simplifying Boolean expressions and hence, for simplifying circuits. Historically, this was what Claude Shannon's paper really meant for electrical