Construct truth trees for the following arguments, then indicate whether the truth tree shows that the argument is deductively valid. (13 points each.)
| 1. |
P
 (Q · S) |
2. |
P
 ~(Q  R) |
|
|
~(Q
R) |
(P
S)
T |
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 |
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|
~P
|
~S
T |
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|
|
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| 3. |
P
~Q |
4. |
~(P
Q) |
|
|
P
R |
~(P
R) |
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|
~Q
R |
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|||
|
|
R
|
|||
|
~R
|
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In each of the following, construct a Venn diagram and use it to answer the question. (12 points each.)
| 5. Some automobiles have diesel engines. No automobiles that have diesel engines burn gasoline. So some automobiles do not burn gasoline. Is this argument valid? |  |
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6. Plato was an ancient Greek philosopher. All ancient Greek philosophers were from Athens or Milos. Plato was not from Milos. So Plato was an Athenian. Is this argument valid? |
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| 7. Casey Jones was not a fireman. All locomotive crewmen were engineers or firemen. Casey Jones was a locomotive crewman. Was Casey Jones an engineer? | |
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8. Not all actors are in movies. All actors who are not in movies audition for commercials. Are all actors who audition for commercials also in movies? |
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