5. (a) Consider the Boolean formula ((AAB) V (AAC)) A (BAC) with assignment to the variables A, B = TRUE, C = FALSE. Evaluate the formula. You do not need to show your work. (b) Consider the Boolean circuit, with assignment to the inputs A, B = TRUE, C = FALSE. Evaluate the Boolean circuit. Show your work by indicating the truth value produced by 10 output each gate. Use the table in the back of this assignment. The senario: You are working as a computer programmer for the Alpha Beta Gamma Software company. It is your dream job. Your manager calls you into the office with the following comment: We hired you because you have a Computer Science degree from one of those fancy colleges. Nobody else here at Alpha Beta Gamma Software has your education or ability. We are moving into the business of Boolean formula evaluation. Starting next month, every morning we will be receiving a large number of large Boolean formulas. For each formula, the assignment of TRUE's and FALSE's to the variables will be given. We will evaluate each formula. We at Alpha Beta Gamma believe that we can rely on you to write a lightning fast program to evaluate these Boolean formulas. You have no idea how to write such a program. You scour the internet but cannot find a satisfactory program to evaluate Boolean formulas. However, you do find a great program to evaluate Boolean circuits. 6. It turns out that it is easy to evaluate Boolean formulas directly in linear time. The spirit of this problem is to avoid doing so! (a) Assume that you are allowed to use the program that evaluates Boolean circuits only once. Briefly explain how you would use the Boolean circuit evaluation program to evaluate a Boolean formula. (b) Show what you would do on the following formula (from Part 4a): ((ANB) V (ANC)) ^ (BAC) Make sure to draw the circuit that is input to the program that evaluates Boolean circuits. 7. Assume the scenario is reversed: You need to evaluate Boolean circuits, but you have a program that evaluates Boolean formulas. Analogously to the previous problem, it is easy to evaluate Boolean circuits directly in linear time. The spirit of this problem is to avoid doing so! (a) Assume that you are allowed to use the program that evaluates Boolean formulas only once. Briefly explain how you would use the Boolean formula evaluation program to evaluate a Boolean circuit. Show what you would do on the circuit in Part 4b. Make sure to state the formula that is input to the program that evaluates Boolean formulas