Last Update: 4 February 2009
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Reminder: Each HW problem solution should consist of:
- a restatement of the entire problem (you may copy it word for word),
- followed by a complete solution with all intermediate steps shown.
- NAME, DATE, RECITATION SECTION AT TOP RIGHT OF
STAPLE MULTIPLE PAGES
All exercises are from §1.4 (nested quantifiers) and §1.5
(rules of inference).
- p. 59: #10 a, b, c, d, e
- Translate English sentences into FOL.
- Be sure to give the syntax and semantics of any new
terms that you have to introduce.
- 3 points each; total = 15 points
- p. 60: #14 a, b, e
- Ditto, but now you have to supply your own predicates.
- To do that, you must give the syntax and semantics of the
predicates you choose.
E.g.: Dog(x) = x is a dog
Loves(x,y) = x loves y
- 3 points each; total = 9 points
Suggestion: #60e is ambiguous; interpret it to mean that
the student has taken all the courses that are offered by a
- p. 60: #20 a, b
- 3 points each; total = 6 points
Below are 5 short arguments in English.
- For each part, first give the syntax and semantics of
translations of each sentence into the language of propositional logic;
e.g., K = "Kangaroos live in Australia."
- Then write each argument in your propositional language.
- Finally, state the rule of inference that validates each
- If Australia is a continent, then it is also an island.
If it is an island, then it is completely surrounded by water.
Therefore, If Australia is a continent, then it is completely
surrounded by water.
- Either New Zealand is a continent or Australia is
a continent. New Zealand is not a continent. Therefore,
Australia is a continent.
- Australia is an island and a continent. Therefore,
it is a continent.
- Europe is an island and a continent. If Europe is an island
and a continent, then so is Australia. Therefore, Australia is
an island and a continent.
- Australia is an island. Therefore, either Australia
is an island, or I'm a monkey's uncle.
- Which, if any, of these arguments are valid? Why?
(2+2=5) → (2 is an odd integer)
Therefore, 2 is an odd integer.
If this is margarine, then I'm a monkey's uncle.
I am a monkey's uncle.
Therefore, this is margarine.
Grand total = 51 points.
Tentative grading scheme:
A 49 - 51
A- 46 - 48
B+ 44 - 45
B 41 - 43
B- 38 - 40
C+ 35 - 37
C 29 - 34
C- 24 - 28
D+ 18 - 23
D 10 - 17
F 0 - 9
DUE: AT THE BEGINNING OF LECTURE, FRIDAY!, FEBRUARY 13|
Copyright © 2009 by
William J. Rapaport