Demonstrate DeMorgan’s Laws using a Venn diagram.

1. Draw a Venn diagram showing the elements of sets A, B, and the universe for all 4 regions.
2. Draw a second diagram showing only the elements of the complement of set A.
3. Draw a third diagram showing only the elements of the complement of set B.
4. Draw a fourth diagram showing the union of steps 2 and 3 for the first DeMorgan’s law or the intersection of steps 2 and 3 for the second DeMorgan’s law.
5. Draw a fifth diagram showing the elements of the intersection of sets A and B for the first DeMorgan’s law or the union of sets A and B for the second DeMorgan’s law.
6. Finally, draw the last diagram showing the complement of step 5. Compare the results from step 4 against those in step 6 to prove both DeMorgan’s laws. In the absence of data elements, you can use 4 different colors to clearly indicate the regions of the universe and follow all of the steps.

Part II

Define two propositions (simple statements that can be either true or false). Give a real-world example of 2 propositions that r and s can represent. Call them r and s. Create a truth table that shows all values of the following:

All work must be completely original as it goes through a turnitin program 

Voting

The ultimate expression of freedom in the United States is the right to vote. This right is deeply treasured by many Americans, but there are those that take the process for granted. How is my vote counted? Do I have fair representation in Congress? Does my vote make a difference? These are the kinds of questions a concerned citizen must ask when considering the voting process. 

There are a number of different methods for counting votes used around the world ranging from majority rule to the constitutionally mandated electoral college used to determine the US presidency. In order to explore the complexities of the voting process and methods used to assure fairness, let’s examine the following scenario:

In the near future, Congress and the states will abolish the process of voting at the polls in the United States. Instead, all citizens will cast their votes via an approved and secure smartphone app.

In your post, address the following questions:

• Describe what changes you anticipate this would make to the accuracy, documentation, expense, and convenience of the voting process.
• What method of fairness do you feel would be best suited to counting the votes in this process: majority rule or some other variation?
• Explain whether this method of voting could be considered truly secure.
• What are some unintended consequences that could arise from this method of casting votes?

When constructing your response, consider the theories, examples, and concepts discussed in your readings this module, and refer to them to support your conclusions.

Write your initial response in a minimum of 200 words. Apply APA standards to citation of sources.

By Saturday, January 10, 2015,