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Unformatted text preview: ( b ) (01111 âˆ§ 10101) âˆ¨ 01000 = 00101 âˆ¨ 01000 = 01101 ( c ) (01010 âŠ• 11011) âŠ• 01000 = 10001 âŠ• 01000 = 11001 ( d ) (11011 âˆ¨ 01010) âˆ§ (10001 âˆ¨ 11011) = 11011 âˆ§ 11011 = 11011 . 1 Prob 1.2.30. We only need to examine the case when the conclusion q âˆ¨ r is false. This is possible if and only if q = F and r = F . But then p âˆ¨ q = F in case p = F , and Â¬ p âˆ¨ r = F in the other case p = T . So, regardless of the value of p , the assumption ( p âˆ¨ q ) âˆ§ ( Â¬ p âˆ¨ r ) is false if q âˆ¨ r is false. Hence this is a tautology. Remark: there are many other ways of solving this problem. Prob 1.3.10. (a) âˆƒ x ( C ( x ) âˆ§ D ( x ) âˆ§ F ( x )). (b) âˆ€ x ( C ( x ) âˆ¨ D ( x ) âˆ¨ F ( x )). (c) âˆƒ x ( C ( x ) âˆ§ F ( x ) âˆ§ Â¬ D ( x )). (d) Â¬âˆƒ x ( C ( x ) âˆ§ D ( x ) âˆ§ F ( x )). (e) âˆƒ xC ( x ) âˆ§ âˆƒ xD ( x ) âˆ§ âˆƒ xF ( x ). 2...
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 Spring '08
 STRAIN
 Math, Logic, Following, The Table, The Conclusion, Assumption of Mary, It's Always Sunny in Philadelphia

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