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xpand then reduce the proposition. Simplify ¬(w∨(p∧¬w)) to ¬w∧¬p Select a law from below to apply to: ¬(w∨(p∧¬w))

xpand then reduce the proposition. Simplify ¬(w∨(p∧¬w)) to ¬w∧¬p Select a law from below to apply to: ¬(w∨(p∧¬w))

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 10CT: Statement P and Q are true while R is a false statement. Classify as true or false:...
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Expand then reduce the proposition.

Simplify ¬(w∨(p∧¬w)) to ¬w∧¬p

Select a law from below to apply to: ¬(w∨(p∧¬w))
### Laws of Logic #### Distributive Laws 1. \((a \land b) \lor (a \land c) \equiv a \land (b \lor c)\) 2. \((a \lor b) \land (a \lor c) \equiv a \lor (b \land c)\) #### Commutative Laws 1. \(a \lor b \equiv b \lor a\) 2. \(a \land b \equiv b \land a\) #### De Morgan's Laws 1. \(\neg (a \lor b) \equiv \neg a \land \neg b\) 2. \(\neg (a \land b) \equiv \neg a \lor \neg b\) #### Conditional Laws 1. \(a \rightarrow b \equiv \neg a \lor b\) 2. \(a \leftrightarrow b \equiv (a \rightarrow b) \land (b \rightarrow a)\) #### Complement Laws 1. \(a \lor \neg a \equiv \text{T}\) 2. \(a \land \neg a \equiv \text{F}\) #### Negation Laws 1. \(\neg \text{T} \equiv \text{F}\) 2. \(\neg \text{F} \equiv \text{T}\) #### Identity Laws 1. \(a \lor \text{F} \equiv a\) 2. \(a \land \text{T} \equiv a\) #### Double Negation Law 1. \(\neg \neg a \equiv a\) This table summarizes fundamental logical equivalences used in Boolean algebra and set theory. These laws are essential for simplifying logical expressions and proving equivalences in logic and mathematics.
Transcribed Image Text:### Laws of Logic #### Distributive Laws 1. \((a \land b) \lor (a \land c) \equiv a \land (b \lor c)\) 2. \((a \lor b) \land (a \lor c) \equiv a \lor (b \land c)\) #### Commutative Laws 1. \(a \lor b \equiv b \lor a\) 2. \(a \land b \equiv b \land a\) #### De Morgan's Laws 1. \(\neg (a \lor b) \equiv \neg a \land \neg b\) 2. \(\neg (a \land b) \equiv \neg a \lor \neg b\) #### Conditional Laws 1. \(a \rightarrow b \equiv \neg a \lor b\) 2. \(a \leftrightarrow b \equiv (a \rightarrow b) \land (b \rightarrow a)\) #### Complement Laws 1. \(a \lor \neg a \equiv \text{T}\) 2. \(a \land \neg a \equiv \text{F}\) #### Negation Laws 1. \(\neg \text{T} \equiv \text{F}\) 2. \(\neg \text{F} \equiv \text{T}\) #### Identity Laws 1. \(a \lor \text{F} \equiv a\) 2. \(a \land \text{T} \equiv a\) #### Double Negation Law 1. \(\neg \neg a \equiv a\) This table summarizes fundamental logical equivalences used in Boolean algebra and set theory. These laws are essential for simplifying logical expressions and proving equivalences in logic and mathematics.
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