7. (20 pts) Use a membership table to show that An (B U Ĉ) = Ã U (B n C), when A, B, and C %3D are sets.
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- (Thermodynamics) The work, W, performed by a single piston in an engine can be determined by this formula: W=Fd F is the force provided by the piston in Newtons. d is the distance the piston moves in meters. a. Determine the units of W by calculating the units resulting from the right side of the formula. Check that your answer corresponds to the units for work listed in Table 1.1. b. Determine the work performed by a piston that provides a force of 1000 N over a distance of 15 centimeters.VII.Let A = {2, 4, 6, 8}, B = {6, 9}, C = {4, 8}. Answer each of the following questions. Justify your answers. 1. Is B ⊆B?7. using c++, Write a void function that accepts an integer array a and a integer SizeA, and an integer n, and adds n to every element in that array. Be sure to develop an appropriate name for your function.
- Explain work a function works with relevant example s4. What does this function return? Which principle does it illustrate?Redo problem 2 where you have to define and use the following functions: (a) isTriangle - takes 3 sides of a triangle and returns true if they form a triangle, false otherwise. (b) isIsosceles - takes 3 sides of a triangle and returns true if they form an isosceles triangle, false otherwise. (c) isEquilateral - takes 3 sides of a triangle and returns true if they form anequilateral triangle, false otherwise. (d) isRight - takes 3 sides of a triangle and returns true if they form a right triangle, false otherwise. (e) your program should run continuous until the user wants to quit this is my problem 2: #include <iostream> #include <cmath> using namespace std; // Constant Declarations const double E = .0001; int main() { double side1, side2, side3; bool isTriangle, isRight, isEquilateral, isIsosceles; cout << "Enter the lengths of the 3 sides of a triangle -- "; cin >> side1 >> side2 >> side3; isTriangle = side1 + side2 > side3 &&side1 +…
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- Redo problem 2 triangle.cc where you have to defineand use the following functions:(a) isTriangle - takes 3 sides of a triangle and returns true if they form a triangle,false otherwise.(b) isIsosceles - takes 3 sides of a triangle and returns true if they form an isoscelestriangle, false otherwise.(c) isEquilateral - takes 3 sides of a triangle and returns true if they form anequilateral triangle, false otherwise.(d) isRight - takes 3 sides of a triangle and returns true if they form a right triangle,false otherwise. this is the question and this is my work for problem 2 // This program prompts a user to enter the lengths of// the 3 sides of a triangle, check if they form a triangle,// and prints the triangle type: right, isosceles, equilateral,// or scalene #include <iostream>#include <cmath> using namespace std; // Constant Declarationsconst double E = .0001; int main() { double side1, side2, side3; bool isTriangle, isRight, isEquilateral, isIsosceles; cout <<…Problem 5: Functions and Sets Let Σ denote a finite alphabet, Σ* denote all words over that alphabet, and L denote the function that maps a string to its length, i.e. L : Σ* → N (where N denotes the natural numbers) [a] Is L partial, total, or both? [b] Is L one-to-one? onto? a bijection? [c] How many words in Σ* have length n? [d] How many words in Σ* have length ≤ n [e] Explain whether Σ* is finite, countable, or uncountable. [f] Explain whether P(Σ*) - the set of all subsets over Σ* - is finite, countable, or uncountable. Hint: how is this related to the real numbers in [0, 1).VII.Let A = {2, 4, 6, 8}, B = {6, 9}, C = {4, 8}. Answer each of the following questions. Justify your answers.20.Is C ⊆ A?21.Is B ⊆ A?22.Is C ⊆ A?23. Is B ⊆B?
