· 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.

- [5 pts] Given the word below, tell what
are stored in the computer memory. We assume our computer uses**characters**__8 bits__to represent a single character. Use the ASCII table and show all of your work. - [5 pts] Given the word below, tell what
(base 10) is stored in the computer memory. We assume our computer uses**decimal number**__16 bits__to represent an integer. Show all of your work. - Write a
__Formal Negation__for the following statements using symbols (/) and variables. There is no partial credit for this problem.- [5 pts] qR such that q < 0 and qq3.
- [5 pts] bZ, if 2 b, then b is odd.

- In the questions below, suppose
*A*= {*a*,*b*,*c*} and*B*= {*a, b,*{*c*}*, d*}.- [5 pts] Is
*A*Í*B*.? Make sure to justify your answer. - [5 pts] Find the power set of
*A*:*P (A)*

- [5 pts] Is
- [5 pts] Show the following number is a rational number. Show all of your work.
- [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.
- [10 pts]
__Disprove__the following statement: - [10 pts] Write a
__proof by contraposition__of the following statement: - You need to show that the following equality is false by doing the following:
- [5 pts] Draw a Venn diagram for each side.
- [5 pts] Disprove the equality

- [10 pts] Write a
__proof by contradiction__of the following statement.