Unformatted text preview: p â†’âˆ¼ q q â†’ r r âˆ§ q âˆ´ âˆ¼ p p q r âˆ¼ q âˆ¼ r p â†’âˆ¼ q âˆ¼ r â†’ q r âˆ§ âˆ¼ q âˆ¼ p T T T F F F T F F T T F F T F T F F T F T T F T T T F T F F T T T F F F F T T F F T T F T F T F F T T T F T F F T T F T T T T F F F T T T F F T This argument is invalid since there exists a critical row with the false conclusion. (Critical row is a row where all the premises are true.) 3. (3pts) Simplify the following (using Theorem 1.1.1). Supply a reason for each step. âˆ¼ ( p âˆ¨ âˆ¼ q ) âˆ¨ ( âˆ¼ p âˆ§ âˆ¼ q ) âˆ¼ ( p âˆ¨ âˆ¼ q ) âˆ¨ ( âˆ¼ p âˆ§ âˆ¼ q ) â‰¡ ( âˆ¼ p âˆ§ âˆ¼ ( âˆ¼ q )) âˆ¨ ( âˆ¼ p âˆ§ âˆ¼ q ) De Morganâ€™s Law â‰¡ ( âˆ¼ p âˆ§ q ) âˆ¨ ( âˆ¼ p âˆ§ âˆ¼ q ) Double Negative â‰¡âˆ¼ p âˆ§ ( q âˆ¨ âˆ¼ q ) Distributive â‰¡âˆ¼ p âˆ§ t Negation â‰¡âˆ¼ p Identity...
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 Spring '10
 seckin
 Logic, critical row, Identity Negation Distributive

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