Articles containing proofs | Rules of inference | Duality theories | Boolean algebra | Theorems in propositional logic
In propositional logic and Boolean algebra, De Morgan's laws, also known as De Morgan's theorem, are a pair of transformation rules that are both valid rules of inference. They are named after Augustus De Morgan, a 19th-century British mathematician. The rules allow the expression of conjunctions and disjunctions purely in terms of each other via negation. The rules can be expressed in English as: * The negation of a disjunction is the conjunction of the negations * The negation of a conjunction is the disjunction of the negations or * The complement of the union of two sets is the same as the intersection of their complements * The complement of the intersection of two sets is the same as the union of their complements or * not (A or B) = (not A) and (not B) * not (A and B) = (not A) or (not B) where "A or B" is an "inclusive or" meaning at least one of A or B rather than an "exclusive or" that means exactly one of A or B. In set theory and Boolean algebra, these are written formally as where * and are sets, * is the complement of , * is the intersection, and * is the union. In formal language, the rules are written as and where * P and Q are propositions, * is the negation logic operator (NOT), * is the conjunction logic operator (AND), * is the disjunction logic operator (OR), * is a metalogical symbol meaning "can be replaced in a logical proof with". Applications of the rules include simplification of logical expressions in computer programs and digital circuit designs. De Morgan's laws are an example of a more general concept of mathematical duality. (Wikipedia).
Probability & Statistics (6 of 62) De Morgan's Law Explained
Visit http://ilectureonline.com for more math and science lectures! In this video I will explain De Morgan's Laws. Next video in series: http://youtu.be/ZuuXPW36OYU
From playlist Michel van Biezen: PROBABILITY & STATISTICS 1 BASICS
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From playlist Sets (Discrete Math)
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In this video I will show you my copy of Formal Logic by Augustus De Morgan. This book was published in 1847 and is considered a collectors item. Note my copy is very hard to read because of the condition of the book but I tried my best to show some of the pages of this old book. You can f
From playlist Book Reviews
MIT RES.6-012 Introduction to Probability, Spring 2018 View the complete course: https://ocw.mit.edu/RES-6-012S18 Instructor: John Tsitsiklis License: Creative Commons BY-NC-SA More information at https://ocw.mit.edu/terms More courses at https://ocw.mit.edu
From playlist MIT RES.6-012 Introduction to Probability, Spring 2018
Proof: DeMorgan's Laws for Set Complement | Set Theory
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Identity, domination idempotent, complementation, commutative, associative, distributive, De Morgan, absorption and complement laws for sets. Textbook: Rosen, Discrete Mathematics and Its Applications, 7e Playlist: https://www.youtube.com/playlist?list=PLl-gb0E4MII28GykmtuBXNUNoej-vY5Rz
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