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Answer each question based only on what was presented in the video lesson. No outside knowledge is needed — all answers can be found in the video.
Apply De Morgan's Laws and negation rules to rewrite logical statements. Show your reasoning for each answer; problems increase in difficulty.
De Morgan's Laws give us clean, precise ways to negate conjunctions, disjunctions, and conditional statements in logic — without awkward phrasing like "it is not the case that." This lesson traces those rules from George Boole's self-taught 19th-century work all the way to the digital circuits powering today's computers. Section 2.6 of Contemporary Mathematics walks through each law step by step, with real-world examples and truth tables to prove the equivalences hold. In this video: • George Boole's 1853 paper, An Investigation of the Laws of Thought, and how it became the foundation of Boolean logic and computer science • De Morgan's Law for negating a conjunction: ~(p ∧ q) ≡ ~p ∨ ~q, explained with a keys-and-wallet analogy • De Morgan's Law for negating a disjunction: ~(p ∨ q) ≡ ~p ∧ ~q, illustrated with the cake-or-ice-cream example • Negating a conditional statement: why ~(p → q) becomes p ∧ ~q, explained through a broken umbrella promise • Applying conditional negation to the Adele Grammy example in plain English • Using truth tables to verify that two logical statements are equivalent via a tautology in the final column #OpenStax #Logic #DeMorgansLaws #BooleanAlgebra #ContemporaryMathematics OpenStax Content adapted from "Contemporary Math", by OpenStax Licensed under CC BY 4.0. Content based on Web Version: Apr 23, 2026. Read the textbook online https://openstax.org/details/books/contemporary-mathematics Music first girl talking to me. by ikkun (ex. Barradeen) | https://soundcloud.com/ikkunwastaken Royalty Free Music by https://www.free-stock-music.com Creative Commons / Attribution-ShareAlike 3.0 Unported (CC BY-SA 3.0) https://creativecommons.org/licenses/by-sa/3.0/deed.en_US
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