CS245 Lecture Notes - Propositional Calculus, Eugenius Warming

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lemoncoyote675

16 Oct 2011

School

University of Waterloo

Department

Computer Science

Course

CS245

Professor

Nancy Day

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Document Summary

Due: thu 22 jan 2009 10am in the cs245 drop boxes. There are multiple correct answers to some of these questions: (9 marks) express each of the following sentences as a formula in propositional logic. W r where: r it rains, w it is winter. Explain your response and demonstrate that your response is correct using the semantics of propositional logic. No, the premises do not logically imply the conclusion. The following boolean valuation, v, is a counterexample where the premises are t and the conclusion is f. v(a) = f, v(b) = t, v(c) = f. Premise 1: v( (b a)) = not (v(b) imp v(a)) Premise 2: v(b c) = v(b) or v(c) In the above boolean valuation, both evaluate to t: (6 marks) use transformational proof to prove: (a b) (b c) c true. (a b) (b c) c ( (a b) (b c)) c impl. (a b) (b c) c dm. (a b) (b c) c.

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: Which of the following are propositions?
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shahasad0133

Programming Writing Montreal Maps In the following questions, you will write classes that allow one to suggest a route to get from one point to another on a metro or train line. Note that for all of these questions, we will make the simplifying assumption that the earth is flat and that everything resides in 2 dimensions. (There were metros before Columbus and Galileo, right?) 6. Write a class MetroStation in which you define a new type MetroStation. (10 points) A MetroStation is defined to have the following private properties: • String name This represents the name of the metro station (e.g. Atwater, McGill, etc) • double xPosition This represents the x location of the metro station. • double y Position This represents the y location of the metro station. An MetroStation object should have the following public methods/behaviors defined on it. • A constructor that takes as input a String stationName, a double x, and a double y. The constructor should initialize the properties name, xPosition, and yPosition to these three values respectively • A method getName() which returns the name of the Metrostation. • A method get XPosition () which returns the x location of the Metrostation • A method get Position () which returns the y location of the Metrostation • A method equals (Metrostation other) which returns a boolean representing whether the name property of the this MetroStation is equal to the name property of other.

29. Consider the Cocktail Sort (code 4) algorithm described in the appendix. What is the fewest number of lines of code that would have to be added, removed, or changed in order for this algorithm to sort from largest to smallest? (A) Everything inside the second for loop. (B) 3 (C) 1 (D) 2 (E) Everything inside both for loops. Binary answers For the following questions you are to use your choices as they were the representation of a binary number. More precisely, A = 24, B = 23, C = 22, D = 21, and E = 20 position in a base 2 number. For example if you wanted to answer the number 23, you would translate it first as base 2 number, which is 10111, you would blacken A, C, D and E.2 Lets look at this process on your answer sheet, we have these 5 circle you can blacken. Normally you only pick one, here you might have to blacken more than one! @ ® © D ® Following the previous example, the answer we want to input is 23, its binary representation is 10111, hence the circle you would blacken are the following:

CS245 Lecture Notes - Propositional Calculus, Eugenius Warming

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