Chapter 20.9, Problem 7P

Translate the following statement into logical expressions using predicates, quantifiers (use the symbols ∀ and ∃) , and logical connectives (use the symbols ¬, ∧, ∨, →). Do not put spaces.   Let A(x)=“x is armed” and D(x)=“x is dangerous”Some dangerous people are not armed. Let M(x)=“x is a Magna Cum Laude” No one is a Magna Cum Laude. Let S(x)=“x is a square” and R(x)=“x is a rectangle” All squares are rectangles. Let E(x)=“x is empathetic” and H(x)=“x will help you” Someone is empathetic or not everyone will help you.

In practical life, the employees get salaries and pay taxes honestly. Sometimes, the process of drawing salariesand payment of taxes may lead to some interesting situation. Suppose, a person draws salary of Rs. 10,000 permonth. A certain percentage of tax is charged on that amount, which is deducted every month. But if the salaryof the person is more than Rs. 10,000 per month, then the tax rate is different. Similarly if a person is getting Rs.20,000 per month, he/she would be charged more under a different tax rate slab. The interesting situationdevelops if there is an anomaly in the tax rates i.e. a person who is getting higher salary takes home lesser moneyas compared to the other person with less gross salary.To further elaborate it, we suppose that there is company 'C' where 100 or less than 100persons are employed. The salaries of the employees and their tax rates are known to us.We are required to list those unlucky persons, who are getting lesser take-home salary(net salary)…

The definitions of "strict" and "loose" name equivalency are given.

Translate the following into MPL: Nice dogs don’t bite unless they are scared.

(Mechanics) The deflection at any point along the centerline of a cantilevered beam, such as the one used for a balcony (see Figure 5.15), when a load is distributed evenly along the beam is given by this formula: d=wx224EI(x2+6l24lx) d is the deflection at location x (ft). xisthedistancefromthesecuredend( ft).wistheweightplacedattheendofthebeam( lbs/ft).listhebeamlength( ft). Eisthemodulesofelasticity( lbs/f t 2 ).Iisthesecondmomentofinertia( f t 4 ). For the beam shown in Figure 5.15, the second moment of inertia is determined as follows: l=bh312 b is the beam’s base. h is the beam’s height. Using these formulas, write, compile, and run a C++ program that determines and displays a table of the deflection for a cantilevered pine beam at half-foot increments along its length, using the following data: w=200lbs/ftl=3ftE=187.2106lb/ft2b=.2fth=.3ft

The mathematical functions introduced in Chapter 4 can be used to compute and simulate engineering and scientific issues. In these cases, we formulate the mathematical issue and then use the computer to perform computations and simulations. Can a computer programme solve a math problem and develop mathematical formulas, i.e., can it perform the functions of a mathematician?

The Philosophers' Dinner Problem Five philosophers sit around a table and spend their lives dining and thinking. Each philosopher has a bowl of noodles and a fork to the left of your plate. To eat the noodles you need two forks and each philosopher you can only take the ones to your left and right. If any philosopher takes a fork and the other is busy, he will wait, fork in hand, until pick up the other fork, so you can start eating later. If two adjacent philosophers try to pick up the same fork at the same time, a race condition: they both compete to take the same fork, and one of them left without eating. If all the philosophers take the fork to their right at the same time, then everyone will be waiting forever, because someone must release the fork that is lack. No one will because everyone is in the same situation (hoping that someone put down their forks). Then the philosophers will starve. This lock mutual is called deadlock or deadlock. The problem is to find an algorithm that…

Define the following sets: A={x, y, z, t}, B={s, t, u, v, w, x}, C={t, v, u, s}, D={s, t, u, v}Determine whether each of the statements is true, false, or meaningless.  State your answer clearly.(You do not have to justify your answers, but they have to be correct.) (a){s, t}⊂D (b)A⊆B (c)A∈C (d)|C|=|B|

Suppose, the pandemic has come to an end and you are ready to join the university once again. In order to accommodate social distancing to provide the students with maximum safety, the authority has divided the students of a section into many classrooms. However, on your first day, you forgot to bring the list of your designated classroom and you don’t have much time to go to the department. But suddenly you remember that your class number is the first nth Fibonacci number. As you don’t have much time, you will have to think of a very fast algorithm for this. Explain your solution.