Jan 24, 2024 Using Venn diagrams, test the following syllogistic forms for validity
Exam 2
Phil/Leap 1250
1 Question 1
Using Venn diagrams, test the following syllogistic forms for validity:
#1.
All M is P
All M is S
———-
All S is P
#2.
Some M is P
Some M is not S
———-
Some S is not P
#3.
Some P is M
Some S is not M
———-
Some S is P
1
2 Question 2
What does it mean for two propositions to be statistically independent? Answer this question by giving both (i) a
formal, probabilistic definition, and (ii) a more intuitive definition in your own words.
3 Question 3
What does it mean for two propositions to be mutually exclusive? Answer this question by giving both (i) a formal,
probabilistic definition, and (ii) a more intuitive definition in your own words.
4 Question 4
Can two propositions be both mutually exclusive and independent? Explain your answer.
5 Question 5
What is the probability of drawing a King from a standard fifty-two-card deck, and then (after replacing the King
to the deck and reshuffling) drawing another King?
2
6 Question 6
If you roll two fair six-sided dice one time, what is the probability that one or the other (or both) of the dice will
come up a five?
7 Question 7
Jim, a famous baseball player, tests positive for steriod use in a random screening of all major leaguers. It is known
that the test used has a ”true positive” rate (the probability that the test will be positive given that the person
does indeed use steroids) of 95% and a ”false positive” rate (the probability that the test will be positive given that
the person does not use sterioids) of 10%. Moreover, it is also known that 10% of major leaguers are steroid users.
What is the probability that Jim really does use steroids given that he tested positive?
8 Question 8
When reasoners judge that a conjunction is more probable than one of its corresponding conjuncts, they are
committing a fallacy. Provide a formal explanation (in terms of probability theory) and an informal explanation
in your own words.
9 Question 9
Only one of the following statements is true. Which one?
A. Every argument that has all true premises and a true conclusion is valid.
B. Every argument that has false premises is invalid.
C. Every argument that has all true premises and a false conclusion is invalid.
D. All of the above statements are actually false.
3
10 Question 10
Using a truth-table, test the following argument form for validity:
#1.
p v q
p ⊃ q
q ⊃ r
———-
r
#2.
(p ⊃ q)&(p ⊃ ¬r)
q&r
———-¬p
#3.
r
———-
(p ⊃ q) v (q ⊃ p)
4
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