PHIL 2303 â€“ Introduction to Formal Logic
Professor Joshua Ellery, J.D., M.A.
Directions: Answer all questions to the best of your ability. Please write ALL of your answers on
this exam paper. Where applicable (e.g., truth tables), SHOW YOUR WORK! I can only award
partial credit if you do so. If you need additional space, please attach your extra page(s) to your
exam. Please verify that your FULL name (first name and last name) is written on the front page
of the exam and, if applicable, any extra pages you give to me.
Part I: True/False Questions â€“ Indicate whether the statement is true or false.
(2 points each; Total exam weight = 10%)
1. The statement “Professor Ellery is either DASHING or HANDSOME.” is an example of an
2. A well-formed formula is a sentence in our symbolic language that has exactly one
interpretation or meaning.
3. All sound arguments are valid.
4. Consider this statement: “I will graduate only if my professor accepts my bribe.” The “I
will graduateâ€¦” portion of the statement is known as the necessary condition.
5. The main connector in the following symbolized statement is the “horseshoe” (âŠƒ):
~[(~P âŠƒ ~Q) â€¢ ~(P v ~Q)]
Part II: Symbolization â€“ Symbolize the following statements, using the abbreviations that have
been provided. Write your answer in the space provided.
(2 points each; Total exam weight = 40%)
6. My girlfriend is SWEET.
7. My girlfriend is SWEET but a PSYCHO.
8. If my girlfriend is a PSYCHO, she is not SWEET.
(Note: P = my girlfriend is psycho; S = my girlfriend is sweet)
9. I have CLIMBED the highest mountains and RUN through fields only to be with you, but I
still haven’t FOUND what I’m looking for. (Note: C = I have climbed highest mountains;
R = I have run through fields only to be with you; F = I have found what I’m looking for)
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10. Jake will not have both COBBLER and PIE.
(Note: C = Jake will have cobbler; P = Jake will have pie)
11. I will PASS logic class if I BRIBE Professor Ellery.
12. Only if I BRIBE Professor Ellery will I PASS logic class.
13. If we INVADE now, there will be WAR and SUFFERING.
14. We will not PROTECT our freedoms unless we INVADE.
(Note: P = we will protect our freedoms; I = we invade)
15. I enjoy WHISKEY or BEER, but not both.
16. I enjoy WHISKEY and BEER; however, I do not like VODKA or TEQUILA.
(Note: W = I enjoy whiskey; B = I enjoy beer; V = I like vodka; T = I like tequila)
17. Janet will TRAVEL to Europe only if she has enough MONEY and she gets neither SICK
nor COLD-FEET. (Note: T = Janet will travel to Europe; M = she has enough money; S =
she does get sick; C = she does get cold-feet)
18. If you think either POISON is cool or TEARS for Fears is good, you are a FOOL and quite
19. Even though neither SOCRATES nor the BUDDHA wrote anything down, many people
ADMIRE them and some people actually LEARN from them.
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20. One of two things will happen: Either Ralphie will DEFEND himself and BEAT up the
bully if he gets ANGRY, FRUSTRATED or MAD enough, or Ralphie will CRY like a wuss
and RUN home to his momma.
21. You should BUY that yacht only if you NEED it, unless you’re RICH and can AFFORD it.
22. Only if either the SKY is falling or I’m offered a MILLION dollars will I WATCH Survivor
or see a BACKSTREET Boys reunion concert.
*** Take a deep breathâ€¦if you put in the work, you got these next ones! ***
23. I will ACE logic if and only if I STUDY hard, complete the HOMEWORK, and I don’t
FAIL the exam, provided that my professor is not a JERK.
(Note: A = I will ace logic; S = I study hard; H = I complete the homework; F = I fail the
exam; J = my professor is a jerk)
24. The Astros will WIN the World Series if only if they do not LOSE the divisional game and
the team stays HEALTHY, provided that if their plane CRASHES, then all BETS are off.
(Note: W = the Astros will win the World Series; L = the Astros lose the divisional game;
H = the team stay healthy; C = their plane crashes; B = all bets are off)
25. The DEFICIT will not be reduced and the economy will neither GROW nor IMPROVE,
provided that JOBS are created or UNEMPLOYMENT does not rise and, second, that either
STOCKS or BONDS show exponential growth.
(Note: D = the deficit will be reduced; G = the economy will grow; I = the economy will
improve; J = jobs are created; U = unemployment does rise; S = stocks show exponential
growth; B = bonds show exponential growth)
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Part III: Truth Tables â€“ Use a truth table to demonstrate whether the two statements below are
materially equivalent or not. Show your truth table and write your answer in the space provided.
(20 points; Total exam weight = 20%)
~P âŠƒ Q and (P v Q) â€¢ (~Q âŠƒ P)
Materially equivalent or not? __________________
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Part IV: More Truth Tables â€“ Use the truth table test for validity to demonstrate whether the
following argument is valid or invalid. Show your truth table and write your answer in the space
provided. Remember: If the argument is invalid, you must indicate which row(s) of the truth table
make it so.
(30 points; Total exam weight = 30%)
~(P â€¢ Q) âŠƒ R
R âŠƒ (P v ~Q)
âˆ´ R â‰¡ ~(P â€¢ Q)
Valid or Invalid? _________________
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