Name __________________________________________
MAT101 – Survey of Mathematical Reasoning
Professor Pestieau
Take-Home Exam 4 – Arguments
Due Date: Tuesday, May 13th
Present all your work neatly on the following problems to receive full credit.
Problem 1
[5 pts each]
For the 7 arguments shown below, proceed as follows:
1) Break down the argument.
Explicitly identify the component statements that are part of the argument and show
the symbolic form of the argument.
2) Analyze it!
Decide whether the argument is valid or invalid. Here you may use truth tables,
standard forms, Euler diagrams, and/or logical manipulation. If the argument is
invalid, point to its logical fallacy.
1.
“If we evolved a race of pure logicians, that would not be progress; but
we have not evolved a race of pure logicians; so that’s progress.”
2.
“Homer is a visionary or he’s a fool; but he’s certainly a fool; so he’s not a visionary.”
3.
“If the fossil is an ammonite, then it is from the Crestaceous period. If the fossil is not
from the Mesozoic era, then it is not from the Crestaceous period. If the fossil is from
the Mesozoic era, then it is at least 65 million years old. Therefore, if the fossil is an
ammonite, it is at least 65 million years old.”
4.
“It’s impossible for pigs to understand logic, and it is also impossible for pigs to breathe
underwater; so it must be the case that pigs neither breathe underwater nor understand
logic.”
5.
This absurd argument is taken from Lewis Carroll’s Symbolic Logic (1896):
“Babies are illogical. Nobody is despised who can manage a crocodile. Illogical persons
are despised. Hence, babies cannot manage crocodiles.”
6.
“No odd number has a factor of 2. Some prime numbers are odd. Therefore, some
prime numbers have a factor of 2.”
[Bonus – Euler Diagram]
7.
“Some whales make good pets. Some good pets are cute. Some cute pets bite. Hence,
some whales bite.”
[Bonus – Euler Diagram]
Problem 2
[5 pts]
Find a valid conclusion to the argument given below in symbolic form. Justify your answer.
~ ( p ~ q )
qr
~r
---------------?
Problem 3
(premise 1)
(premise 2)
(premise 3)
(conclusion)
[3 pts]
Determine, by any means, whether the following argument is valid or not:
“If a set A is a proper subset of another set B, then the intersection of A and B is also a
proper subset of B; but A is equal to B or B is a proper subset of A; hence the
intersection of A and B is a proper subset of A.”