Homework
Translating into Propositional Form
Exercise 1:
Review the following sentences and their translation. (In this exercise, there is no need to
write anything down.)
1. Obama ran for office in 2012.
O
2. Obama did not run for office in 2012.
~O
3. Obama and Romney ran for office in 2012.
O = Obama ran for office in 2012
R = Romney ran for office in 2012
OR
4. John or Rich will bring the pie.
J = John will bring the pie.
R = Rich will bring the pie.
OvR
5. If John brings the pie, Rich will bring the appetizer.
J = John brings the pie.
R = Rich brings the appetizer.
JR
6. I will be happy if and only if I go to Disneyland.
H = I will be happy.
D = I go to Disneyland
HD
7. John or Rich will bring the dessert, and Sally will bring the appetizer.
J = John will bring the dessert.
R = Rich will bring the dessert.
S = Sally will bring the appetizer.
(J v R)  S
8. If John or Rich bring the dessert, then Sally will bring the appetizer.
J = John will bring the dessert.
R = Rich will bring the dessert.
S = Sally will bring the appetizer.
(J v R)  S
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9. If you ace the midterm and ace the final, you will ace the class.
M = You ace the midterm
F = You ace the final.
P = You will pass the class
(M  F)  P
10. If you don’t ace the midterm, you will not ace the class.
M = You ace the midterm
C = You will ace the class.
~M C
11. If Kate Winslet and Jessica Biel do a comedy, then either Forest Whitaker will make a
documentary or Paris Hilton will do a skin flick.
K = Kate Winslett does a comedy.
J = Jessica Biel does a comedy.
F = Forest Whitaker will make a documentary.
P = Paris Hilton will do a skin flick.
(K  B) (F v P)
12. It is not the case that both Iran gives up its nukes and Syria or Pakistan combats
terrorism.
I = Iran gives up its nukes
S = Syria combats terrorism
P = Pakistan combats terrorism
~[I  (S v P)]
Exercise 2:
For the following:
(a) Label each proposition using a capital letter of your choice.
(b) Write down the connectives involved.
(c) Provide a translation in propositional form
Be sure to label parts (a), (b), (c) clearly in your responses.
Example: It is not the case that either Hezbollah will renounce violence or Al Qaeda and the
Taliban will be defeated.
(a) H = Hezbollah will renounce violence; A = Al Qaeda will be defeated; T = The
Taliban will be defeated
(b) ~ v 
(c) ~ [H v (A T)]
1. The Giants won the World Series in 2010 and 2012.
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2. It is not the case that Mitt Romney won the election
3. Plato wrote The Republic and Aristotle wrote The Nicomachean Ethics.
4. If Democrats win the White House in 2012, the U.S. will not invade Syria.
5. It is not true that Socrates wrote books or it is not true that Zeno wrote books.
6. Either you win or you lose, and not both.
7. Hitler ran the Third Reich and Nixon did not resign the presidency.
8. Lincoln wrote the Gettysburg Address if and only if France bombed Pearl Harbor
9. It is false that the earth is at the center of the universe and it is false that the sun revolves
around the earth.
10. If Hitler ran the Third Reich, then either Custer was killed by the Indians or Einstein
discovered aspirin.
11. If the 49ers win on Sunday and the Cowboys lose, I will be happy.
12. Either Sonia Sotomayor or Antonin Scalia have a modern approach to the Constitution,
but it is not the case that both do.
13. Either Mariah Carey sings pop and Elton John sings rock, or Diana Krall sings jazz.
14. Neither Ferrari nor Maserati makes economy cars.
15. Saturn has rings, and Neptune is windy or Jupiter is massive.
16. Saturn has rings and Neptune is windy, or Jupiter is massive.
17. Tiffany and Ben Bridge will release an emerald collection unless Zales and Kay do not.
18. Barack Obama emphasizes peaceful negotiation; but if North Korea starts a war, then
either China or Japan will be involved.
19. It is not the case that both Iran gives up its nuclear program and Syria or Pakistan
combats terrorism.
20. If Spike Lee writes a screen play, then if Denzel Washington stars in the movie, then
Paramount and MGM will compete to produce it.
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