1. What is a Boolean Variable? 2. Create a table demonstrating the Boolean Operations complement, addition, and multiplication. { ,+,} note: you can use ' instead of the overline in this project for complement 3. Calculate the result for the boolean function: f(x,y) = xy + xy for the following inputs: Hint: Can you find column for this function on table 3 above? x x x x = = = = 1 1 0 0 and and and and y y y y = = = = 1 0 1 0 : : : : f(1,1) f(1,0) f(0,1) f(0,0) = = = = ? ? ? ? 4. How many Boolean functions on two variables are there? 5. What does functionally complete mean? 6. What is a literal? Given the Boolean Variables x and y, what are the associated four literals? 7. What is a minterm? Given the Boolean Variables x and y, what are the associated four minterms? Identify the four functions that correspond to each minterm in table 3 8. What is disjunctive normal form? Given the Boolean Variables x and y, give the Boolean function in disjunctive normal form for functions F9 and F11. Hint: Look to question 3 as an example of what a function should look like. Demonstrate Hint: Look to Question 3 as an example of what a function should look like. 9. Using the variables x and y, list all the Boolean functions on two variables as the sum of minterms. Functions written in other forms will not be eligible for full credit. Hint: Questions 3, 7, and 8 should have almost halfway through the list. 10. Using the propositions P and Q, translate the equivalent characterizations of your Boolean functions as compound logic propositions. Translate from your list above and do not simplify (they should still be in Disjunctive Normal Form). Bonus Question: Prove 11. You read that {, +, } is functionally complete. Demonstrate that {} is functionally complete