A) Diagram the following arguments:
1.
[1Joe has a good chance of passing only if he studies]. But [2unless
the weather worsens, Joe will not study]. Hence, since [3the weather
does not worsen], [4Joe does not have a good chance of passing]. (3 points)
2.
[1Unless the rainforests are preserved, there will be an ecological
disaster]. For, [2only if biodiversity is maintained can there be
a decent quality of life on this planet]. Hence, [3we should fight
the oil companies which destroy the equatorial rainforest]. (3 points)
3.
[1The son did it]. For, [2either the son or the butler did it].
[3 If the butler did it, the fingerprints on the poison bottle must be
his]. But [4the fingerprints on the poison bottle don’t match the butler’s],
and therefore [5they are not his]. But then, since [6if the son did
it, Joe is innocent], [7Joe should be free]. (4 points)
B) Translate the follwing sentences using the following vocabulary:
S=it snows; C=it’s cold; J=Joe goes out; P=Joe will pass; W=Joe
studies; R=the Rams play. (2 points each)
1. It snows only if it’s cold
2. Joe doesn’t pass unless he studies, and he studies only if it snows.
3. If it snows, then Joe studies unless the Rams play.
4. Joe doesn’t study, and Joe passes.
5. The Rams play only if it doesn’t snow, but Joe doesn’t study unless
it’s cold.
C. Check the following arguments for validity without using a truth table. (15 points each)
1.
F->(-GvH)
F->G
-(HvI)
------------
F->J
2.
(-HvJ)vK
K-> -I
-------
(H&I)->J
D. Answer the following multiple choice questions. (5 points each)
1. Only one of the following is true. Which one?
a. In a valid argument, the premises are true
b. In an invalid argument, the conclusion is false
c. In a valid argument, the conclusion is true
d. none of the above.
2. Only one of the following is true. Which one?
a. “A&-A. Hence B” is invalid.
b. “B. Hence A&-A” is valid.
c. (A->B) is the same as (is logically equivalent to, i.e. has the
same truth table as) -AvB
d. none of the above