Mathematics for Computer Science

3.4. The Algebra of Propositions 53 Three axioms that don’t directly correspond to number properties are AANDA! A (idempotence f ...

Chapter 3 Logical Formulas54 Using distributivity over bothAND’s we get ..AANDA/OR.BANDA//OR..AANDC/OR.BANDC//: By the way, we’v ...

3.5. The SAT Problem 55 Theorem 3.4.4. Any propositional formula can be transformed into disjunctive normal form or a conjunctiv ...

Chapter 3 Logical Formulas56 n^2 orn^14 —instead ofexponentially— 2 n—whether any given proposition of sizen is satisfiable or n ...

3.6. Predicate Formulas 57 is always true whenxis a real number. That is, 8 x 2 R:x^2  0 is a true statement. On the other hand ...

Chapter 3 Logical Formulas58 or maybe you can solveat least oneproblem we come up with. (3.18) To be precise, let Probs be the s ...

3.6. Predicate Formulas 59 Or it could mean that every American has a personal dream: 8 a 2 A 9 d 2 D:H.a;d/ For example, some A ...

Chapter 3 Logical Formulas60 The corresponding predicate formula equivalence is NOT. 9 x:P.x// is equivalent to 8 x:NOT.P.x//: ( ...

3.7. References 61 We hope this is helpful as an explanation, but we don’t really want to call it a “proof.” The problem is that ...

Chapter 3 Logical Formulas62 QWWDYou do every exercise in the book. RWWDYou get an A in the class. Translate following assertion ...

3.7. References 63 or equivalently, H IFF T: Explain why it is reasonable to translate these two IF-THEN statements in dif- fere ...

Chapter 3 Logical Formulas64 This 2-bit half-adder could be described by the following formulas: c 0 Db s 0 Da 0 XOR c 0 c 1 Da ...

3.7. References 65 (a)A 1-bitadd1module just has inputa 0. Write propositional formulas for its outputscandp 0. (b)Explain how t ...

Chapter 3 Logical Formulas66 .nC1/-bit add 1 2.nC2/-bit add 1 module .nC1/-bit add 1 a2nC 1 anC 2 anC 1 rn r 1 r 0 an a 1 a 0 p2 ...

3.7. References 67 Problems for Section 3.3 Practice Problems Problem 3.8. Indicate whether each of the following propositional ...

Chapter 3 Logical Formulas68 Class Problems Problem 3.11. (a)Verify by truth table that .P IMPLIES Q/ OR.Q IMPLIES P/ is valid. ...

3.7. References 69 (b)Demonstrate that this set of specifications is satisfiable by describing a single truth assignment for the ...

Chapter 3 Logical Formulas70 Homework Problems Problem 3.16. Use the equivalence axioms of Section 3.4.2 to convert the followin ...

3.7. References 71 (a)Explain why theANDof the four constraining formulas above along with a fifth formula consisting of just th ...

Chapter 3 Logical Formulas72 8 x 9 y: x2yD 0 8 x:x < 10IMPLIES. 8 y: y < xIMPLIESy < 9/ 8 x 9 y: Œy > x^9z: yCzD100 ...