MATH 3500 Lecture Notes - Unary Operation, Truth Table, Propositional Variable

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lavendercod225

9 Jan 2014

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A proposition is a statement of fact that can be determined true or false, a propositional variable is a letter assigned to represent a proposition. Most commonly p and q p: it is raining q: 3+5=8 negate these with the ! or ~ symbol as in !p or ~p (read: not p: example: q: there are at least 12 students in the class. !q: there are greater than 12 students in the class. Negating a proposition involves using proper english grammar to state the opposite of the proposition, or what would make the original proposition false: truth table for the not (!) operator: p. The not symbol is a unary operator, meaning it operates on only one number. p: it is raining. q: 3+5=8. ^ is the and symbol p^q means p and q. This is true only when both p and q are true.

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Practice 12-2 Conditional Probability 1. The table contains information about Education and Salary of Employees the 1205 employees at one business. Find Under S20,000 to Over each probability. Round to the nearest $20,000 $30,000 S30,000 tenth of a percent. Less than high school 69 36 2 a. P(employee has less than a high High School 112 98 14 school education) 102 103 143 b. P(employee earns under $20,000) Some college c. P(employee earns over $30,000 13 178 25 College degree and has less than a high school education) d. P(employee earns under $20,000 and has a college degree) given that th e employee has on ly a high school education, the probability that the employee earns over $30,000 f. given that the employee earns over $30,000, the probability that the employee has only a high school education or less 2. High school students in one school chose their favorite leisure activity. Find each probability. Round to the nearest tenth of a percent. Favorite Leisure Activities Sports Hiking Reading Phoning Shopping other 48 85 02 71 29 Female 39 Male a. P(sports female b. P(female l sports) c. P(reading l male d. P male l reading) g. male I shopping) h. P(female shopping) e. P(hiking I female) f. P(hiking l male) 3. The senior class is 55% female, and 32% are females who play a competitive sport. Find the probability that a student plays a competitive sport, given that the student is female. Draw a tree diagram. Find each probability 4. A softball game has an 80% chance of being canceled for a light drizzle and a 30% chance of being canceled for a heavy fog when there is no drizzle. There is a 70% chance of heavy fog and a 30% chance of t drizzle. a. Find the probability that the game will be canceled b. Find the probability there will be a light drizzle and the game will not be canceled. The students of a high school are 51% males: 45% of the m ales and 49% of the females attend concerts. a. Find the probability that a student attends concerts. b. Find the probability that a student is a female and does not attend concerts.

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8. Write a class called WordSet representing a set of String objects which can contain an arbitrary number of strings, limited only by the memory available to the Java Virtual Machine. A set is a collection of elements, however, unlike a list, a set cannot contain duplicate elements. Therefore, as its name implies, a WordSet object cannot contain duplicate Strings that is, if one attempts to da String to a Wordset, and the wordset already contains an element which is equal to this string, the attempt will fail and the state of the Wordset will not change. All String comparisons performed in the methods defined in the Wordset class are done in a Case SENSITIVE manner. Note that in the method descriptions below, the phrase "this Wordset" means "the Wordset on which the method in question is called." Your Wordset class MUST provide the following INSTANCE methods • A constructor, which takes no parameters and initializes the new Wordset ohject so that it contains no elements • A method called add(), which takes as its only parameter a string and returns a value of type boolean. If this Wordset already contains a string which is equal to the parameter string, or the parameter String is null, then the state of this Wordset does not change and the method return false; otherwise, the parameter String is added to this Wordset. and the method returns true. • A method called remove().which takes as its only parameter a string and returns a value of type boolean. If this wordSet contains a string which is equal to the parameter String this string is removed from the WordSet and the method returns true. On the other hand, if the string parameter is null or this Wordset does not contain a string which is equal to the parameter string, then the state of this wordset does not change, and the method return false. • A method called get.size(), which takes no parameters and returns the number of strings currently stored in this Wordset. This method MUST NOT change the state of this Wordset. • A method called isMember(). which takes as its only parameter a string and retumsa value of type boolean which is true if this wordset contains the parameter String false otherwise. If the parameter String is null, this method also return false. This method MUST NOT change the state of this wordset. • A method called computebirrerence().which takes as its only parameter a Wordset and returns a new Wordset representing the difference between this wordset and the parameter Wordset: in other words, the WordSet returned by this method contains all the strings that are in this wordset, but not in the parameter Wordset. If the parameter Wordset contains all the elements of this WordSet or this WordSet contains no elements, then this method returns a new Wordset containing no elements. Finally, if the parameter Wordset is null or contains ne strings, then this method returns a new wordset which contains all the elements of this wordset. This method MUST NOT change the state of this wordset or the parameter Wordset. • A method called tostring , which takes the parameters and turns a string which is the textual representation of this wordset. This textual representation consists of the concatena tion of the following clements - The String - The text representation of each clement in the WordSet; cach pair of adjacent clements is separated by the String", but this String MUST NOT appear before the first clement or after the last element - The String") The order in which the elements of this Wordset appear in the textual representation generated by the tostring() method does not matter. If the WordSet contains to Brings, then the textual representation returned by this method is ". Note that you MUST respect proper encapsulation practices that is, the attributes and methods of your class MUST be declared using the proper visibility modifier NINT Um an array list (of string) to keep track of the string stored in a wordt ob joot Is there a method defined in the Array loist class which determines whether in clementis already wored in an array ist, and which will do a case-sensitive comparison when liked on an Arraylint of strings? See the pages 24-26 of this examination for information about potentially useful methods defined by the ArrayList class WRITE YOUR Wordset CLASS IN THE SPACE BELOW:

MATH 3500 Lecture Notes - Unary Operation, Truth Table, Propositional Variable

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