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PHIL 111: Inductive Logic
Class
problems
Chapters 2, 6, and 4
Chapter 2: Induction
a. Population to sample: Ex.
b. Sample to population: Ex.
c. Sample to sample: Ex.
d. Argument from authority: Ex.
e. Testimony: Ex.
f. Inference to the best explanation: Ex.
g. Decision theory: Ex.
Chapter 6: The basic rules of probability
Rule 1: If a proposition is a tautology, then the probability is equal to 1.
Rule 2: If a proposition is a selfcontradiction, then the probability is equal to 0.
Rule 3: If two propositions are logically equivalent, then they have the same probability.
Suppose that the Pr(p) = ½ and Pr(q) = 1/4 .
Find the probabilities of the following complex statements
using Rules 13 and the Boolean truth table method. As well, indicate the rule that you used to
determine the probability.
a. p
∨
p
b. q
∧
q
c. q
∧
~q
d. ~(q
∧
~q)
e. ~(p
∨
~p)
f. ~~(p
∨
~p)
g. p
∨
(q
∧
~q)
h. q
∧
(p
∨
~p)
Rule 4 [additivity]: If p and q are mutually exclusive, then the Pr(p
∨
q) = Pr(p) + Pr(q)
Ex. What is the probability of drawing a two or five on a fair die?
Rule 5: Pr(~p) = 1 – Pr(p)
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 Fall '08
 Everett

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