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
Answer the following questions. Present your answers in a MSWord Document named LastName_FirstInitial_Proj1.
Research
What is a Boolean Variable?
Create a table demonstrating the Boolean Operations complement, addition, and multiplication. { ¯,+,·}
note: you can use ’ instead of the overline in this project
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) = ?
How many Boolean functions on two variables are there?
What does functionally complete mean?
What is a literal? Given the Boolean Variables x and y, what are the associated four literals?
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.
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.)