CS 281 Solutions to Test 1

1(a) tex2html_wrap_inline25
(b) tex2html_wrap_inline27
(c) tex2html_wrap_inline29
or equivalently tex2html_wrap_inline31
(d) tex2html_wrap_inline33
Also tex2html_wrap_inline35
(e) tex2html_wrap_inline37
Also tex2html_wrap_inline39

2(a) tex2html_wrap_inline41
(b) tex2html_wrap_inline43
(c) tex2html_wrap_inline45 , tex2html_wrap_inline41
(d) tex2html_wrap_inline41
(e) P

3(a) (1) tex2html_wrap_inline53 , tex2html_wrap_inline55
(2) tex2html_wrap_inline57 , tex2html_wrap_inline59
(3) tex2html_wrap_inline61
(4) tex2html_wrap_inline63

Converse:
(3) If it is snowing, then it is below freezing.
(4) If it is below freezing, then it is snowing.
Neg. (1) If it is not snowing, then it is below freezing.
Neg. (2) If it is snowing, then it is below freezing.

Contrapositive:
(3) If it is not snowing, then it is not below freezing.
(4) If it is not below freezing, then it is not snowing.
Neg. (1) If it is snowing, then it is not below freezing.
Neg. (2) If it is not snowing, then it is not below freezing.

4(a) I: IBN will take over the copier market.
Y: Yerox will take over the copier market.
R: RCB returns to the computer market.

tex2html_wrap_inline65
tex2html_wrap_inline67
---------------
tex2html_wrap_inline69

(b) tex2html_wrap_inline65
tex2html_wrap_inline73 -- De Morgan
------------------- by modus ponens
tex2html_wrap_inline75
tex2html_wrap_inline77 -- Simplification
------------------- by modus ponens
tex2html_wrap_inline79
tex2html_wrap_inline67
------------------- by modus tollens
tex2html_wrap_inline69




S. Toida
Fri Jun 5 18:05:27 EDT 1998