Q3 Let U = {5, 6 }, write an equivalent to the following assertions: 3x P ( x ) v - Vx Q ( x ) Q4. Ex. : letU = I, and N (x): " E (x): O (x): P (x): x is a nonnegative integer x is even " ; x is odd " ; x is prime " express the following assertions in logical notation The only even and prime must be two For all numbers, if an integer is not even, then it is odd
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A: Answer : True
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A: I have given an answer in step 2.
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A: I have given an answer in step 2.
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- Q3: Interplanetary Spaceflight Milan Tusk is the richest person in the universe. After devoting decades of his life to further our space exploration technologies, he’s finally ready to retire. Being a space enthusiast, the first thing he wants to do is visit n planets p1, p2, …, pn, in this order. He’s currently on planet p0. Milan knows that the distance between planets pi and pi + 1 (for 0 ≤ i < n) is d[i]light years. His spaceship uses 1 tonne of fossil fuels per light year. He starts with a full tank and can fill up his tank at any of the n planets (but he must not run out in between two planets). There’s a huge cost to set up the spaceship for refuelling. Due to financial constraints (he’s not THAT rich), he can fill up his tank at most ktimes. In order to save money and make his spaceship lighter, Milan is looking for the smallest possible fuel tank that enables him to complete his space travel and reach planet pn. What is the smallest tank capacity that enables him to do so?…Ex: Let A1 ={x, y}, A2 ={1, 2}, and A3 ={a, b}, Find A1 × A2, (A1 × A2) × A3, A1 × A2 × A3.7. We usually write numbers in decimal form (or base 10), meaning numbers are composed using 10 different "digits" {0,1,.9). Sometimes though it is useful to write numbers in hexadecimal or base 16. Now there are 16 distinct digits that can be used to form numbers: {0,1,..,9,A,B,C,D,E,F}. So, for example, a 3 digit hexadecimal number might be 3B8. (a) How many 2-digit hexadecimals are there in which the first digit is E or F? Explain your answer in terms of the additive principle (using either events or sets). (b) Explain why your answer to the previous part is correct in terms of the multiplicative principle (using either events or sets). Why do both the additive and multiplicative principles give you the same answer? (c) How many 3-digit hexadecimals start with a letter (A-F) and end with a numeral (0-9)? Explain. (d) How many 3-digit hexadecimals start with a letter (A-F) or end with a numeral (0-9) (or both)? Explain.
- irses/135852/quizzes/807844/take/questions/13768818 inal Exam A+ arted: Jun 17 at 10:03pm Quiz Instructions Show Instructions D 00 1 pts Question 5 Let p, q, and r be propositional variables. After simplification using equivalence laws, p^ (p v ¬¬(r⇒ q)) becomes ____ Op ^ (r+q) OP OT Op ^ q < Previous Next ▸ Il app.honorlock.com is sharing your screen. Stop sharing Hide Your Webcam JUN tv ♫ NA 30 17 F5 F6 80 F3 F4 F7 (((( DII F8 8£ NLet S = {1, 2, 3, ..., n). Consider the following two statements: 1. If 12 is odd, then S has the same number of subsets with an odd number of elements as subsets with an even number of elements. 2. If 72 is even, then S has the same number of subsets with an odd number of elements as subsets with an even number of elements. Which of the following is correct? Statement 1 is true and Statement 2 is false. Statement 1 is true and Statement 2 is true. Statement 1 is false and Statement 2 is false. Statement 1 is false and Statement 2 is true.2. For each of the following sets, determine whether each of these statements is true or false. Write T or F. _e. {x} C {x} f. {x} C {{x}} g. {x} € P({{x}}) _h. {x} C P({x}) La. 0 E Ø _b. {0} C Ø _c. Ø E {0} _d. {ø} C {Ø, {Ø}}
- 3. Write a recursive function that ассepts 8x8 array of an characters that represents a maze. Each position can contain either an X or a blank. Starting at position (0,1), list any path through the maze to get to the location (7,7). Only horizontal and vertical moves are allowed. If no path exists, write a message indicating there is no path. Moves can be made only to the locations that contain a blank. If an X is encountered, that path is blocked and another must be chosen. [6]AIM: TO SWAP 2 NUMBERS WITHOUT USE OF TEMPORARY VARIABLE THEORY: C is a general-purpose, middle level, procedural computer programming language supporting structured programming, lexical variable scope, and recursion, with a static type system. C is an imperative procedural language. Let a and b be variables in which integral values are being inserted . tw numbers can be swapped without using a temporary variable by using arithmetic operations. Another alternative method is by use of logical operators. ALGORITHM: STEP 1: Start STEP 2:Print "Enter two numbers'" STEP 3: Input x,y STEP 4:Print “ Numbers x,y before swapping STEP 5: x x+y STEP 6: y<– x-y STEP 7: x x-y STEP 8: Print “ Numbers x,y after swapping " STEP 9: StopDomain: Set of real numbersWhat is the truth value of each of these statements. Justify each answer with substantive explanations and not just generic True/False answers.1) ∀x(x2 − 1 > 0) 2) ∃x∃y(x4 + y4 = 0)
- 2. For arbitrary set B explain why each of the following statements is either true or false. (a) BCP(B) (b) B = P(B) 3. Jimmy St. Udent claimed that P({red, blue}) is equal to {red, blue, {red, blue}, Ø}. Explain why Jimmy is either correct or incorrect.Download the file Ackermann.cpp. Inside the file the recursive Ackermann function is implemented (described in Chapter 14 Programming Challenge 9). Do the following and answer the three questions: a) Run the program. What happens?b) Now uncomment the code that is commented out and run the program again. What happens now?c) What do you think is going on?If Q(x) is the statement x + 1 > 2x, and the domain is the set of positive integers, which of the following best characterizes the following two statements : A) there exists x such that Q(x) is true B) for every x, ¬Q(x) is true Only A is true O Only B is true O Both A and B are true O Both A and B are false