1. Interpreting Quantified Statements Group 4 questions 1.1 Is this statement True of False Choose One 3 points Consider the statement, "For all real numbers x, the result of x2 is even." Is this statement true or false? True False 1.2 Is this statement true or false? Choose One 3 points Consider the following statement \"For all real numbers x, the result of x2 is a positive number\". Is this statement true or false? It is True because a multiplication is only negative when the one number is positive and the other is negative. It is False because 0 is not a positive number, so 0 squared is not positive 1.3 Which of the following are true? Choose all that apply 4 points Let P(x): The word x contains the letter 'a'. P(Apple) P(Orange) P(Lemon) P(True) P(False) 1.4 Which of the following are true Choose all that apply 4 points Let T(x):x1 ) Recall that the notation that P(x) is true !x P(x) means that there is a unique x such True False 3.4 What is the Truth Value of the following Choose One 3 points Consider the domain of all integers. What is the truth value of !x ( x+3=2x ) Recall that the notation that P(x) is true. True False !x P(x) means that there is a unique x such 4. Identify the Opposite (Negation) Group 3 questions 4.1 Identify the negation of the following quantified statement: Choose One 3 points "Some phones have high definition cameras" Some phones do not have high definition cameras All phones do not have high definition cameras All phones have high definition cameras 4.2 Identify the negation of the following quantified statement: Choose One 3 points "All NFL teams have their own stadium" No NFL team has its own stadium Some NFL teams have their own stadiums There is an NFL team that does not have its own stadium 4.3 Identify the negation of the following quantified statement: Choose One 3 points "Some student will not turn in their projects" Some students will turn in their projects All students will turn in their projects No student will turn in a project 5. Identify the Negation (Symbolically) Group 3 questions 5.1 Select the equivalent form for the following quantified statement: Choose One 3 points x P(x) x P(x) x P(x) x P(x) x P(x) 5.2 Select the equivalent form for the following quantified statement: Choose One 3 points x P(x) x P(x) x P(x) x P(x) x P(x) 5.3 Select the equivalent form for the following quantified statement: Choose One 3 points x (P(x)Q(x)) x (P(x)Q(x)) x (P(x)Q(x)) x (P(x)Q(x)) x (P(x)Q(x)) 6. Evaluate Multi Variable Predicates Group 2 questions 6.1 What is the truth value of the following statement? Choose One 3 points The information in this problem refers to World of Warcraft at launch (before any expansion) In Warcraft, there are two playable factions: Horde and Alliance. The Warlock class is available to the Horde races: Orc, Undead, Troll (but not Tauren), and the Alliance races: Human, Dwarf, Gnome (but not Night Elf). Consider the domain of all races for Let: x and the domain of all factions for y. W(x,y): The warlock class is available to the x race on the yfaction. A table reprsenting the information above What is the truth value of the following statement? x y W(x,y) True False 6.2 What is the truth value of the following statement? Choose One 3 points The information in this problem refers to World of Warcraft at launch (before any expansion) In Warcraft, there are two playable factions: Horde and Alliance. The Warlock class is available to the Horde races: Orc, Undead, Troll (but not Tauren), and the Alliance races: Human, Dwarf, Gnome (but not Night Elf). Consider the domain of all races for Let: x and the domain of all factions for y. W(x,y): The warlock class is available to the x race on the yfaction. A table representing the information above What is the truth value of the following statement? x y W(x,y) True False 7. Interprete Multi Variable Predicates Group 2 questions 7.1 Select the symbolic representation: Choose One 3 points Given the predicate: E(x,y): Character class x can equip y weapon Identify the symbolic representation for the following sentence: "There is a character class which can not equip any weapon" xy E(x,y) xy E(x,y) xy E(x,y) xy E(x,y) 7.2 Select the symbolic representation: Choose One 3 points Given the predicate: system version y S(x,y): x app will work on operating Identify the symbolic representation for the following sentence: "Some apps will not work in the current version of the operating system" xy S(x,y) xy S(x,y) xy S(x,y) xy S(x,y) 8. Determine the Validity of an Argument Group 4 questions 8.1 Is the following logical argument valid? Choose One 3 points If the device is connected to a charger then the software will check for updates The device is connected to a charger Therefore the software will check for updates Yes - It is valid No - it is not valid 8.2 Is the following logical argument valid? Choose One 3 points If the player collects 100 coins they will earn an extra life The player earned an extra life Therefore the player collected 100 coins Yes - the argument is valid No - the argument is not valid 8.3 Is the following logical argument valid? Choose One 3 points A potion restores health or mana The potion did not restore health Therefore the potion restores mana Yes - the argument is valid No - the argument is not valid 8.4 Is the following logical argument valid? Choose One 3 points Opening the golden chest will award a player the ultimate sword The skeleton key or magic lockpick will open the golden chest The player was awarded the ultimate sword The player has the skeleton key Therefore the player does not have the magic lockpick Yes - the argument is valid No - the argument is not valid 9. Convert from Decimal Group 2 questions 9.1 Convert the number 19 from Decimal to Binary Choose One 3 points 0000 1101 0001 0101 0001 0001 0001 0011 9.2 Convert the number 150 from Decimal to Binary Choose One 3 points 1001 0110 0110 1001 1001 1001 0110 0110 10. Convert from Binary Group 2 questions 10.1 Convert 0001 1011 from Binary to Decimal. Choose One 3 points 23 24 27 26 10.2 Convert 1111 1000 from Binary to Decimal Choose One 3 points 124 240 248 496 11. Hexadecimal Conversions Group 2 questions 11.1 Convert 1101 1001 0101 1011 from Binary to Hexadecimal. Choose One 4 points 55,643 139,511 EA 6C D9 5B C8 4A 1.2 Convert 4C3 from Hexadecmial to Decimal Choose One 4 points 1219 1235 19760 MCMLXXIX 10011000011