(4) 4. Let P(x,y)= "x sent a text message to y." The u.d. for both x and y is all people. Translate into symbols: a. Everyone has sent a text message to someone. b. Everyone has been sent a text message by someone.
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- 38. The geometric mean g of n numbers x; is defined as the nth root of the product of x;: g=Vx1x2X3•…Xn (This is useful, for example, in finding the average rate of return for an investment which is something you'd do in engineering economics). If an investment returns 15% the first year, 50% the second, and 30% the third year, the average rate of return would be (1.15*1.50*1.30)") Compute this.2. Let A(x) be the statement "x has apples," C(x) be the statement "x has cherries," and B(x, y) be the statement "x is better than y," where the domain of x and y consists of all pies. Which logical expression corresponds to the following statement? "There is some pie that has apples that is better than every pie that has cherries." a. 3xVy(A(x) ^ (C(y) → B (x, y))) b. xvy(A(x)^C(y) ^ B (x, y)) c. xvy((A(x) ^ C(y)) → B (x, y)) d. 3xVy(A(x) → (C(y) ^ B (x, y)))3. Let K(x) be the statement “x has a pet koala,” let G(x) be the statement “x has a gazelle," let U(x) be the statement "x has a unicorn," and let F(x) be the statement "x has a farm." Express each of these statements in terms of K(x), G(x), U(x), F(x), quantifiers, and logical connectives. Let the domain consist of all people. (a) Everyone owns a gazelle or a unicorn. (b) Any person who does not own a farm cannot own a koala, gazelle, or unicorn. (c) No one owns a gazelle, but everyone owns a koala. (d) Some people own both a unicorn and a farm, but not all people own both a koala and a gazelle. (e) Each type of animal (koala, gazelle, unicorn) is owned by at least one person.
- Question 9 Electrical resistors are said to be connected "in series" if the same current passes through each and "in parallel" if the same voltage is applied across each. If in series, they are equivalent to a single resistor whose resistance is given by + R₂ R = R₁ + R₂ + R3 + If in parallel, their equivalent resistance is given by 1 1 1 1 1 = + + + + R₁. R R₁ R₁ R₂ Write an M- le that prompts the user for the type of connection (series or parallel) and the number of resistors n and then computes the equivalent resistance.(2) Let P (x, y) : x plays in y." A(x) : x is athletic." S(x) :x is smart." E(y) : y is in English league." F (y) : y is famous." Assume the domain of x is all players and the domain of y is all football teams. Answer the following questions. (a) Write the symbolic for: Some smart and athletic players play in some English league teams (b) Write the English for: 3y A(MohamedSalah) ^ E(y) ^ P (MohamedSalah, y). (c) Rewrite the statement starting with "Some... ": Not all smart players play in some famous teamsHeat capacity of a solid: Debye's theory of solids gives the heat capacity of a solid at temperature T to be 3 T rOp/T Cy = 9VpkB (e* – 1)2 dx, - where V is the volume of the solid, p is the number density of atoms, kg is Boltzmann's constant, and 0D is the so-called Debye temperature, a property of solids that depends on their density and speed of sound. Develop a computer code to evaluate Cy (T) for a given value of the temperature, for a sample consisting of 1000 cubic centimeters of solid aluminum, which has a number density of p = 6.022 x 1028m-3 and a Debye temperature of 0p = 428K. The Boltzmann's constant kg = 1.380649 x 10-23 J · K-1. Please evaluate the integral with the following methods: (a) MATLAB adaptive Simpson quadrature, [Q.FCNT] = QUAD(FUN,A,B,TOL) with TOL =le-10.
- Let x, y, and z be True statements, and a, b, and c be False statements. If (x m) V (y ^ b) = False, then m =[Fish Tank] You play with a clown fish that has an initial size so. The fish can eat other fish in a tank organized in m columns and n rows. The fish at column i and row j has a positive size si,j. When your fish eats another fish, it grows by that amount. For example, if your clown fish has a size of 10 and eats a fish of size 5, it becomes of size 15. You cannot eat a fish that is bigger than your size. The game starts by eating any fish in the first (left-most) column that is not bigger than yours. After that, you advance one column at a time by moving right. You have only three allowed moves. You either stay at the same row, move one row higher or one row lower. You will always move to the right. Thus, you will make exactly m moves to advance from left to right. Your goal is to exit the fish tank from the right with the biggest possible size. The figure below shows an example with the best answer highlighted. In this case, the final fish size is 71 (10+8+7+24+22). You are required…Step 1 (2 pts). Read from input student status (String), homework points, quiz points, midterm exam score, and final exam score (double). Valid student status includes undergrad (UG), grad (G), and distance leaner (DL). Calculate each category average using maximum points for homework (800), quizzes (400), midterm exam (150), and final exam (200). Output an error message if student status is not one of the three options. Otherwise, output category averages as a percentage using System.out.printf("Homework: %.1f%%", homework). Submit for grading to confirm two tests pass.
- 5. We are given the statement "C3PO is a droid and Han is not a droid". (a) Using the following statement variables, write the corresponding statement form: Let p = "C3PO is a droid" and q = "Han is a droid" (b) Using De Morgan's Laws, develop the negation of the statement form of part (a) (c) What is the statement that corresponds to the statement form of part (b)?6.) Write the regular expression that can match only complete words which have repeating letters. Assume the words contain only lower-case letters. Example words that would match are pizza, smooth, and hawaii. The correct solution must implement the back-reference expression. For example, no credit will be given for solutions with regular expressions having 26 or statements. There is only one word per line and partial words cannot be matched.A year in the modern Gregorian Calendar consists of 365 days. In reality, the earth takes longer to rotate around the sun. To account for the difference in time, every 4 years, a leap year takes place. A leap year is when a year has 366 days: An extra day, February 29th. The requirements for a given year to be a leap year are: 1) The year must be divisible by 4 2) If the year is a century year (1700, 1800, etc.), the year must be evenly divisible by 400 Some example leap years are 1600, 1712, and 2016. Write a program that takes in a year and determines whether that year is a leap year. Ex: If the input is: 1913 the output is: 1913 - not a leap year Code: is_leap_year = Falseinput_year = int(input()) 'Your code here'