Chapter 4 Review Exercises
ex III

1. Which of the following is a good symbolization of "Neither the French nor the Germans wins a match". (Symbolizing in the obvious way.)
F>~G
~F&G ~(FvG)
~(F&G)
2. Which of the following is a good symbolization of "If one of the teams (form France, Germany and Denmark) wins, the other two lose."?
G>~(FvD)
[Gv(FvD)]>[~G&(~F&~D)]
(G>~(FvD)&[(F>~(DvG)&(D>~(FvG)]
[(Gv(FvD))>(~G&(~F&~D))]&[G>~(FvD)]
3. Which of the following is a good symbolization of "At most one of the teams wins"?
G>~(FvD)
(Gv(FvD))>(~G&(~F&~D))
(G>~(FvD)&[(F>~(DvG)&(D>~(FvG)]
[(Gv(FvD))>(~G&(~F&~D))]&[G>~(FvD)]
4. What thought do you need to add to make the English statement of question 3 say "Exactly one of the teams win"? That is, which of the following do you need to add to "At most one wins" to get the idea that exactly one wins?
"the Germans didn't win"
"at least one team wins"
"no team loses"
"at most two teams win"
5. There is a nice simple way to express "At most two teams win". How would you symbolize that?
~F&(G&D)
~F&~(G&D)
(~F&~G)&~D
(~Fv~G)v~D

Score =
Correct answers: