4. Last night Kerry’s backpack was lost. You are assigned to figure out who kept
ID: 3114016 • Letter: 4
Question
4. Last night Kerry’s backpack was lost. You are assigned to figure out who kept the backpack or if it is in Kerry’s dorm and the whereabouts of Enoch and Gigi. You have the following information:
(i) Hanna claims that Carl did not find the backpack or that Frank was not on campus that day.
(ii) Later it was determined that Hanna was not telling the truth.
(iii) If Carl found the backpack, then he either took it to Kerry’s dorm or gave it to Andy.
(iv) Either Andy or Ben have the backpack or it is in Kerry’s dorm.
(v) Enoch going bowling that night is a necessary condition for Andy taking the backpack.
(vi) If Frank was on campus, then he took Enoch bowling.
(vii) Gigi going to sleep early is a necessary condition for Enoch going bowling and Andy keeping the backpack.
(viii) The backpack was not in Kerry’s dorm.
(a) Translate each of the statements above into symbolic logic using the variables below:
Variable Deifinition
A:
B:
C:
D: The backpack is in Kerry’s dorm.
E:
F:
G: Gigi went to sleep early.
(b) Use rules of inference AND NAME THEM, to deduce your conclusion about the backpack.
Conclusion:
Explanation / Answer
Answer(a)
The statements can be translated as below:
A. Enoch went bowling.
B. Andy took the backpack.
C. The backpack is not in Kerry's dorm.
D. The backpack is in Kerry’s dorm. (given)
E. Carl found the backpack.
F. Hanna is lying.
G. Gigi went to sleep early. (given)
Answer(b)
Rule No. 1 - If F is true, THEN E follows.
Rule No. 2 - If E is true, THEN D or B follows.
Rule No. 3 - If D is true, THEN a conclusion about the backpack is reached.
Rule No. 4 - If B is true, THEN G, A and C are necessarily true. C concludes that backpack is not in Kerry's dorm.
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