· You MUST type all of your answers for each question in the space provided. 

· For full credit, you need to show all of your work when requested.

· You MUST save your exam file as “LastName, FirstName – Final” and place it in the Drop Box before the deadline specified in the ENGAGE online course shell. Note that you have a total of 6 hours (typed answers only) OR 80 minutes (handwritten answers) once you access the exam file.

· You can easily insert symbols by copying & pasting what you need from the following list. 

1. [5 pts] Given the word below, tell what characters      are stored in the computer memory. We assume our computer uses 8 bits      to represent a single character. Use the ASCII table and show all of your      work.
2. [5 pts] Given the word below, tell what decimal      number (base 10) is stored in the computer memory. We assume our      computer uses 16 bits to represent an integer. Show all of your      work. 
3. Write a Formal Negation for the      following statements using symbols (/) and      variables. There is no partial credit for this problem.
   1. [5 pts] qR such       that q < 0 and qq3.
   2. [5 pts] bZ, if 2 b,       then b is odd.
4. In the questions below, suppose A = {a, b, c} and B = {a, b, {c}, d}.
   1. [5 pts] Is A Í B.? Make sure to justify       your answer.
   2. [5 pts] Find the power set of A: P       (A)
5. [5 pts] Show the following number is a      rational number. Show all of your work.
6. [10 pts] Use the Euclidean algorithm to      calculate the greatest common divisor of the following pair of integers:      2431 and 4131. Show all of your work. 
7. [10 pts] Disprove the following      statement:
8. [10 pts] Write a proof by contraposition      of the following statement:
9. You need to show that the following      equality is false by doing the following:
   1. [5 pts] Draw a Venn diagram for each       side.
   2. [5 pts] Disprove the equality
10. [10 pts] Write a proof by contradiction      of the following statement.