There are more questions below than what you need to hand in. You choose, which ones to hand in.

Submit for marking a total of 15 solutions to questions (not more). Of the questions that you hand in, 13 need to be analytically solved (handwritten or typeset) and 2 need to be Mathematica based questions.

Each analytic question weights 6pts/100; each Mathematica based question weighs 11pts/100.

In your hand-in, please try and order the questions in ascending order. Also, for each question please try to note both the number of the question as appearing below as well as the example number. It is best if you place the Mathematica based questions last, making sure to submit both Mathematica code and output.

1. Example 89.
2. Example 90.
3. Example 91.
4. Example 92.
5. Example 94.
6. Example 95.
7. Is it true that 6 | 2a(3b+3) for all integer a,b?
8. Is 2a(4b+1) a multiple of 4 for all integer a,b?
9. Example 96.
10. Let k,a,b be integers. Assume that k|a and k|b. Prove that k|(a+b).
11. Example 97.
12. Example 98.
13. Example 99.
14. Example 100.
15. Example 101.
16. Example 104.
17. Example 106.
18. Example 108b.
19. Example 111.
20. Example 112.
21. Prove by induction the formula for the sum of the first squared integers (1^2+2^2+....+n^2).
22. Prove by induction that 1+2^(2n-1) is divisible by 3.
23. Example 113.
24. Example 114.
25. Example 115.
26. Construct the truth table for the statement, (p or q) and (~ p).
27. Investigate the statement (p and q) or (~p or (p and ~q)). Is it a tautology, a contradiction or neither?
28. Show using truth tables that "and" and "or" are both commutative and assoicative.
29. Example 116.
30. Example 117.
31. Example 118.
32. Read about the Boolean satisfiability problem and summarize the main concept of this problem in 2 paragraphs.