## Explore the underlying structure that unites Logic and Set Theory.

Explore the underlying structure that unites Logic and Set Theory.

Outline

• Read Chapter 9 Research:Boolean Algebra • Answer the questions below. Refer to

the attached for table, for questions 6&7.

Instructions

Research

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

3. Calculate the result for the boolean function: f(x,y) = (x∙y) + (x∙ȳ) for the following inputs

x = 1 and y = 1 : f(1,1) = ?

x = 0 and y = 1 : f(0,1) = ?

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 from the Table 3 that correspond to each minterm.
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.

Demonstrate

9. Using the variables x and y, create a table listing all the Boolean functions on two variables. Be sure to give them in disjunctive normal form. All other formats will earn 0 points.

10. Using the propositions P and Q, list the equivalent characterizations of your Boolean functions as compound propositions. Translate from your list above and do not simplify.

Bonus Question: Prove

You read that {·, +, ¯} is functionally complete. Demonstrate that {↓} is functionally complete. (You should provide evidence/proof of any equations you write here.)