Review of Truth Tables and De Morgan s Rules. Bradley Kjell (Revised 03/30/2010)

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Wendy Hoover
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1 Review of ruth ables ad De Morga s Rules. Bradley Kjell (Revised 03/30/2010) 1. Complete the followig truth table: Operad Operad Expressio x <= y y > 100 x <= y y > 100 Decide from the table what the value of the expressio is is whe x == 150 ad y == 125. / 2. Complete the followig truth table: Operad Operad Expressio ch >= 'a' ch <= 'z' ch >= 'a' && ch <= 'z' Decide from the table what the value of the expressio is whe ch == 'A'. / 3. Complete the followig truth table: Operad Operad Operad Subexpressio Expressio ch >= 'a' ch <= 'z' ch == '?' ch >= 'a' && ch <= 'z' (ch >= 'a' && ch <= 'z') ch == '?' Decide from the table what the value of the expressio is whe ch == 'x'. / Used by permissio. Page 1 of 5

2 4. Is!A && B equivalet to A!B? Complete the table to fid out. Operad Operad Subexpressio Subexpressio Expressio Expressio A B!A!B!A && B A!B he two expressios are equivalet if the / values i the last two colums are the same. Are the two colums the same? Now use De Morga's Rule:!(A && B) is equivalet to!a!b to rewrite!(!a && B ). 5. You wish to purchase a certificate of deposit, but oly if the iterest rate is greater tha three percet ad the miimum deposit is less tha ill i the blaks. if ( iterest 3 miimum 10000) System.out.pritl("Reject this CD"); Rewrite the above fragmet so that it fits the followig. if ( iterest 3 miimum 10000) System.out.pritl("Reject this CD"); (he first program fragmet is probably the best way to write this.) 6. A program is searchig for books with a call umber that starts "QA" Used by permissio. Page 2 of 5

3 published betwee 1990 ad 1995 (iclusive) with the word "web" i the title. Assume that the attributes of a book are accessed by book.getitle(), book.getdate(), ad book.getcall(). Recall that idexof( Strig sub ) returs the iteger idex of the substrig, or -1 if the substrig is ot foud. if ( book.getcall().idexof("qa") 0 book.getdate() 1990 book.getdate() 1995 book.getitle().idexof("web") 0 ) System.out.pritl( book.getcall(), book.getitle() ); Used by permissio. Page 3 of 5

4 Aswer Key 1. Operad Operad Expressio x <= y y > 100 x <= y y > 100 Decide from the table what the value of the expressio is whe x == 150 ad y == Operad Operad Expressio ch >= 'a' ch <= 'z' ch >= 'a' && ch <= 'z' Decide from the table what the value of the expressio is whe ch == 'A'. 3. Operad Operad Operad Subexpressio Expressio ch >= 'a' ch <= 'z' ch == '?' ch >= 'a' && ch <= 'z' (ch >= 'a' && ch <= 'z') ch == '?' Decide from the table what the value of the expressio is whe ch == 'x'. Used by permissio. Page 4 of 5

5 4. Operad Operad Subexpressio Subexpressio Expressio Expressio A B!A!B!A && B A!B he two expressios are equivalet if the / values i the last two colums are the same. Are the two colums the same? No they are opposites Now use De Morga's Rule:!(A && B) is equivalet to!a!b to rewrite!(!a && B ). A!B 5. if ( iterest > 3 && miimum < 10000) System.out.pritl("Reject this CD"); Rewrite the above fragmet so that it fits the followig. if ( iterest <= 3 miimum > 10000) System.out.pritl("Reject this CD"); 6. if ( book.getcall().idexof("qa") >= 0 && book.getdate() >= 1990 && book.getdate() <= 1995 && book.getitle().idexof("web") >= 0 ) System.out.pritl( book.getcall(), book.getitle() ); Used by permissio. Page 5 of 5

English Bible for the Deaf

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