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Expand then reduce the proposition. Simplify ¬(¬q→(¬p∧¬q)) to ¬q∧p Select a law from below to apply to: ¬(¬q→(¬p∧¬q))

Expand then reduce the proposition. Simplify ¬(¬q→(¬p∧¬q)) to ¬q∧p Select a law from below to apply to: ¬(¬q→(¬p∧¬q))

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Expand then reduce the proposition.

Simplify ¬(¬q→(¬p∧¬q)) to ¬q∧p

Select a law from below to apply to: ¬(¬q→(¬p∧¬q))
 
 
### Logical Laws This table presents important logical laws used in mathematical logic and computer science. #### Distributive Laws - \((a \land b) \lor (a \land c) \equiv a \land (b \lor c)\) - \((a \lor b) \land (a \lor c) \equiv a \lor (b \land c)\) #### Commutative Laws - \(a \lor b \equiv b \lor a\) - \(a \land b \equiv b \land a\) #### De Morgan's Laws - \(\lnot (a \lor b) \equiv \lnot a \land \lnot b\) - \(\lnot (a \land b) \equiv \lnot a \lor \lnot b\) #### Conditional Laws - \(a \rightarrow b \equiv \lnot a \lor b\) - \(a \leftrightarrow b \equiv (a \rightarrow b) \land (b \rightarrow a)\) #### Complement Laws - \(a \lor \lnot a \equiv \text{True}\) - \(a \land \lnot a \equiv \text{False}\) - \(\lnot \text{True} \equiv \text{False}\) - \(\lnot \text{False} \equiv \text{True}\) #### Identity Laws - \(a \lor \text{False} \equiv a\) - \(a \land \text{True} \equiv a\) #### Double Negation Law - \(\lnot \lnot a \equiv a\) These laws are fundamental in simplifying logical expressions and proving logical equivalences.
Transcribed Image Text:### Logical Laws This table presents important logical laws used in mathematical logic and computer science. #### Distributive Laws - \((a \land b) \lor (a \land c) \equiv a \land (b \lor c)\) - \((a \lor b) \land (a \lor c) \equiv a \lor (b \land c)\) #### Commutative Laws - \(a \lor b \equiv b \lor a\) - \(a \land b \equiv b \land a\) #### De Morgan's Laws - \(\lnot (a \lor b) \equiv \lnot a \land \lnot b\) - \(\lnot (a \land b) \equiv \lnot a \lor \lnot b\) #### Conditional Laws - \(a \rightarrow b \equiv \lnot a \lor b\) - \(a \leftrightarrow b \equiv (a \rightarrow b) \land (b \rightarrow a)\) #### Complement Laws - \(a \lor \lnot a \equiv \text{True}\) - \(a \land \lnot a \equiv \text{False}\) - \(\lnot \text{True} \equiv \text{False}\) - \(\lnot \text{False} \equiv \text{True}\) #### Identity Laws - \(a \lor \text{False} \equiv a\) - \(a \land \text{True} \equiv a\) #### Double Negation Law - \(\lnot \lnot a \equiv a\) These laws are fundamental in simplifying logical expressions and proving logical equivalences.
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