1. How many Boolean functions on two variables are there?
2. What is a literal? Given the Boolean Variables x and y, what are the associated four literals?
3. What is a minterm? Given the Boolean Variables x and y, what are the associated four minterms?
4. What is a sum-of-products? Given the Boolean Variables x and y, give an example of a Boolean function in sum-of-products form.
5. Using the variables x and y, list all the Boolean functions on two variables. Be sure to give them in sum-of-products form. All other formats will earn 0 points.
6. Using the propositions P and Q, list the equivalent characterizations of your Boolean functions as compound propositions. (The textbook covers this explicitly.)
7. Using the sets A and B, list the equivalent characterizations of your Boolean functions as Set Theoretic statements. (The book does not cover this, but the process is trivial: simply substitute ∩ for · and substitute ∪ for +.)
8. In #6 you listed 16 distinct compound propositions. We know it is possible to write a compound proposition that does not appear on this list. Write one. Find a proposition from #6 that is equivalent to your proposition.
9. What does functionally complete mean? 10. You read that {·, +, ï¿£} is functionally complete. Demonstrate that {↓} is functionally complete. (You should provide evidence/proof of any equations you write here.)