Problem Set 2
2 points

The problems are taken from the text. Keep in mind starred problems have solutions in the back!

Chapter 1.3
Exercises #3 (all), 6 (all), 8 (a,d,h,j), 10 (a,e,h,k), 11 (a,b,c)

Chapter 1.4
Exercises #1(c,d), 4 (all)

Select Solutions
1.3
3 (a) There exists an integer k such that n=2k.
(b) There exists an integer k such that n=2k+1
(c) There exists an integer k such that b=ak
(d) n>1 AND for all k, ~(there exists) an integer a such that (a>1 and a is not n, and n=ka).
(e) n=1 OR there exist integers a,b>1 such that n=ab.

10(e) TRUE.
Keep in mind the order of the quantifiers. The last "exist" quantifier means that for each choice of y, you needt o have an x that makes the equation true FOR ALL possible choices of z.  Such an x is actually just 0 (and it is the same for all choices of y, even though in theory it wouldn't have to be).

1.4
4 (c) Many of you used the converse of (ii), claiming that if Plum is guilty, then it took place at midnight. This is not true! (ii) tells you what happens if the crime happened at midnight, but if it happens at noon, (ii) tells you nothing.
Correct answer: Since the crime was committed with the revolver, it was not committed with the candlestick. Thus Miss Scarlett is innocent by (iii). Therefore by (v) Professor Plum is guilty.