CS 281 Solutions to Test I
July 16, 1996


1. (a) tex2html_wrap_inline19
(b) tex2html_wrap_inline21
(c) tex2html_wrap_inline23
(d) 2 is even.
(d) E(2)
(e) tex2html_wrap_inline29

2. Fill in the blanks with the shortest string of characters so that the resultant proposition is valid.

(a) tex2html_wrap_inline31 , tex2html_wrap_inline33
(b) tex2html_wrap_inline35
(c) tex2html_wrap_inline31
(d) 0

3 (a) tex2html_wrap_inline41
tex2html_wrap_inline43
tex2html_wrap_inline45
tex2html_wrap_inline47
tex2html_wrap_inline49
tex2html_wrap_inline51
(b) tex2html_wrap_inline53
tex2html_wrap_inline55 tex2html_wrap_inline57
tex2html_wrap_inline55 tex2html_wrap_inline61
tex2html_wrap_inline55 1

4. Find the converse and contrapositive for each of the following propositions:
Converses:
(a) If an argument is not valid, then it is wrong.
(b) If the largest number in a list of numbers can be found quickly, then the list is sorted.
(c) if 3 is not divisible by 2, then it is a prime number.
Contrapositives:
(a) If an argument is valid, then it is not wrong.
(b) If the largest number in a list of numbers can not be found quickly, then the list is not sorted.
(c) if 3 is divisible by 2, then it is not a prime number.




S. Toida
Thu May 29 10:42:57 EDT 1997