1. Prove formally that the following statements are equivalent: For any two formulas A and B, (a) A = B; (b) A → B is valid; (c) A^¬B is unsatisfiable.

Suppose that the binary operator + is overloaded as a member function for the . How many parameters does the function operator+ have? (5, 6) Suppose that the binary operator && is overloaded as a nonmember function for the . How many parameters does the function operator&& have? (5,6)

Consider the definition of the class product Type as given in Exercise 8. Answer the following questions. (1, 2, 3, 5, 7) a. Write the definition of the function set so that instance variables are set according to the paramaters. Instance variables quantitieslnStock, price, and discount must be nonnegative. b. Write the definition of the function print to output the values of the instance variables. c Write the definition of the function setQuantitiesInStock to set the value of the instance variable quantitiesInStock according to the parameter. d. Write the definition of the function updateQuantitiesInStock to update the value of instance variable quantitiesInStock by adding the value of the parameter. e. Write the definition of the function getQuantitiesInStock to return the value of instance variable quantitiesInStock. f. Write the definition of the function setPrice to set the value of the instance variable price according to the parameter. g. Write the definition of the function getPrice to return the value of the instance variable price. h. Write the definition of the function setDiscount to set the value of the instance variable discount according to the parameter. i. Write the definition of the function getDiscount to return the value of the instance variable discount.

Assume the definition of the classes employee and hourlyEmployee as given in Exercise 9. (2, 3, 4) After identifying and correcting errors in the definition of the class hourlyEmployee, give its correct definition. Determine whether the function setPay of the class hourlyEmployee overrides or overloads the function setPay of the class employee. After correcting errors, if any, in the definition of the class hourlyEmployee, write the definition of the member functions of the class hourlyEmployee.

(Program) Write a program that tests the effectiveness of the rand() library function. Start by initializing 10 counters, such as zerocount, onecount, twocount, and so forth, to 0. Then generate a large number of pseudorandom integers between 0 and 9. Each time 0 occurs, increment zerocount; when 1 occurs, increment onecount; and so on. Finally, display the number of 0s, 1s, 2s, and so on that occurred and the percentage of time they occurred.